case study on wireless network

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Case Studies New Wireless Network Access Control Solution

New Wireless Network Access Control Solution

This wireless network access control solution helped this public school district in Maryland prepare for the future with a new controller, access points, switches, and upgrades to the existing infrastructure.

What Data Networks Did for TCPS

• Delivered a comprehensive solution for wireless network access, including upgrades to the existing infrastructure.
• Performed a site survey and technical assessment for the current network.
• Redesigned the network for scalability to support a one-to-one initiative and further growth.
• Procured, staged, installed, and configured Aruba controller & APs and Juniper EX Series switches.
• Leveraged existing cabling infrastructure to reduce costs.

The challenge

Talbot County Public Schools (TCPS), located in Maryland’s eastern shore, devotes a significant portion of its academic learning improvement plan to complying with the Maryland High School Assessments (HSAs) requirements. The HSAs are three tests (algebra/data analysis, biology, and English) that comprise one part of Maryland’s graduation requirements. An emphasis must be placed on learning and preparing to pass these exams, for which TCPS has developed a four-year improvement plan to ensure success.

In an effort to ensure that every student demonstrates improved academic achievement, TCPS instituted a one-to-one computing initiative which provides each its Easton High School students with an Apple laptop computer to encourage technology-based learning. TCPS was then faced with a range of challenges to ensure their users have reliable and secure wireless access.

Talbot County Public Schools enlisted Data Networks to implement a complete wireless network solution, from design to installation and configuration. An emphasis was placed on keeping existing core network equipment and cabling infrastructure, while positioning the core network for growth. In addition, TCPS needed a solution that could scale as more schools upgrade, with central management from EHS, and allow appropriate and secure access for students, teachers, staff, and guests.

The solution

Data Networks performed a site survey and developed a new Wireless SAN solution and related infrastructure upgrade at Easton High School, providing professional services related to the staging, installation, configuration, testing, and project management necessary for implementing this solution. Leaning on our premier partners Aruba and Juniper, Data Networks designed a solution that supplies the performance, security, management, and scalability TCPS needed at the lowest TCO.

The Aruba portion of the solution included:

• Installation and configuration of a new Aruba Networks 6000 series
• Wireless Controller
• Upgrade to latest supported version of ArubaOS
• Replacement of existing Access Points with 80 new Aruba AP-125 802.11ABGN dual-radio access points

The Juniper portion of the solution included:

• Installation of four (4) new Juniper EX4200 Ethernet switches in existing equipment rack in the MDF; two (2) new Juniper EX4200 Ethernet switches in the server room and one (1) Juniper EX3200 Ethernet switch in each of the three existing IDFs
• Upgrade to the latest supported version of JUNOS
• Configuration of 802.11 trunk port on one 10GE uplink (SFP + LRM) to the existing Cisco switch
• Configuration of switch stacks in a Virtual Chassis for centralized management
• An end-to-end test of the wired and wireless networks

Mission accomplished

Using a dynamic configuration deployment method, the existing network was leveraged to provide the configuration details needed for access points to locate and communicate with the mobility controller to receive a software image, initial configuration parameters, and post-deployment configuration. The controller contains an integrated network management system that configures, controls, and operates all mobility controllers and access points in the entire network, and allows for up-to 512 access points as the network expands.

“To position TCPS with a scalable solution, Data Networks was able to provide secure wireless network access and integrate upgrades to the existing infrastructure,” says Dwayne MacKenzie, Data Networks’ Networking & Security Solutions Architect. “The EHS students, teachers, staff, and guest users now enjoy fast, secure wireless with minimal impact on the TCPS technology staff.”

Click here to view the PDF version of the New Wireless Network Access System Helps Talbot County Public Schools Prepare for the Future case study .

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Designing a Wireless Network

Table of contents, chapter 8: designing a wireless campus network: university case study, introduction.

This chapter will take you through the detailed steps in designing a wireless campus network . The steps in this chapter are paramount to the success of any wireless design and implementation project. This chapter will describe the basic characteristics of a campus network, and what we use to define a campus architecture. After reading this chapter, you should have enough information to determine if the project you are working on fits into the campus model. We will also uncover the potential pitfalls in designing and implementing a wireless network and the capabilities available to overcome those issues. In general, our use of the term campus refers to a university, hospital, or company that resides in an area such that all the buildings in that area belong to the organization; the hospital case study in Chapter 6 focused on the particular needs of a medical facility in avoiding problems with interference. A typical requirement of campus networks is the increased mobility or an always connected capability for the individuals present at that campus. Note also that although we use the term campus in the subsections, these principles pertain to all wireless network designs in varying degrees.

Applying Wireless Technology in a Campus Network

There are numerous benefits to using a wireless campus network over a traditional wireline network in this type of environment. Benefits include cost savings: no labor cost for digging trenches and limited time stringing cable. With wireless technology, you can rapidly deploy a new...

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Case Studies

As WiFi specialists, we’ve designed, installed and configured wireless solutions for a range of organisations including schools, warehouses, offices, councils, events venues, caravan parks, hospitals, and many more. Our case studies below highlight why our clients chose to invest in upgrading their networks, how we approached the unique challenges they faced, and how we found a solution with their business’ growth in mind.

If you would like to speak to any of our clients regarding their experience of working with Redway, please get in touch with us – we’d be happy to arrange it.

"Hazel 4D As experts in packaging across the U.K. and Europe, Hazel 4D relies on a vast range of technologies and machinery to drive its supply chain. In early 2024, the business moved to a high-spec warehouse and distribution centre, requiring a new wireless network within a tight timescale, as well as a project that […]"

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Leverhulme Trust

"Leverhulme Trust It wasn’t just slow speeds that were impacting Leverhulme Trust’s 3,000 users. Their 10 year old mixed estate network was both inflating the time taken to manage the Trust’s network, and increasing the risk of a major security breach. The Department of Education’s Connect the Classroom programme supported the school in transitioning to […]"

Chorus Education Trust

"Chorus Education Trust With over 2,000 students across just 2 of its campuses – and the number of schools expanding – the foundations for EdTech and digital education needed to be future-proofed at The Chorus Education Trust. The Department of Education’s Connect the Classroom programme supported the school in transitioning to a future-proof Wi-Fi 6 […]"

Manor Lodge School

"Manor Lodge School With immersive classrooms, IoT adoption and outdoor learning spaces, Manor Lodge School in Hertfordshire is at the forefront of educational transformation, thanks to a future-proofed wireless network from Redway Networks. The school has seen a tenfold increase in Wi-Fi speeds, permitting the bandwidth necessary to support EdTech well into the future, improving […]"

Anthem Schools Trust

"Anthem Schools Trust As one of the most well-established Trusts in the U.K., Anthem Schools Trust prioritises an educational experience that supports its 6,700 students reaching their potential. This is increasingly delivered through digital platforms and resources, requiring a robust network ready for the future of learning – both in terms of performance and ease […]"

Great Baddow High School

"Great Baddow High School Seamless, personalised 1:1 learning for over 1,600 pupils, total network visibility, and streamlined management – all underpinned by cloud-managed WiFi 6. The school’s student experience includes first-class educational and recreational resources where collaboration – on and offline – are strongly supported. Their future-focused strategy relies on connectivity capable of supporting these […]"

Drybrook Primary School

"Drybrook Primary School Digital Education Benefits Learning Outcomes at Drybrook Primary School With over 200 pupils from pre-school to year 6, Drybrook Primary School – part of the Forest of Dean Trust in Gloucestershire – sees its role in bringing technology into classrooms as vital in preparing students for their next steps in education. Building […]"

Dene Magna & Drybrook

"Dene Magna & Drybrook Smart CCTV Brings a New Vision to Dene Magna & Drybrook Schools Dene Magna Secondary School and Drybrook Primary School are part of the Forest of Dean Trust, and with over 1200 students and 100 staff across their campuses, keeping the sites secure is vital. Both schools had CCTV in place, […]"

Reedbut Group

"Reedbut Group Improves Efficiency Across Nationwide Warehouses with Next-Gen Wi-Fi from Redway Networks As one of the leading sheet plant manufacturers of eco-friendly packaging, Reedbut Group must respond to tight delivery demands across the UK, Europe and the wider world. This relies on seamless warehouse operations with increasing amounts of tech hardware and software, from […]"

Forest of Dean Trust

"Forest Of Dean Trust A full stack Cisco Meraki solution delivers a future-proofed IT foundation for a secure, supportive, superior digital learning environment. The new cloud-managed solution – including switches, Wi-Fi, physical and network security – will support the Trust in adopting the latest educational tools, reducing network management time, securing against the rising numbers […]"

Horsham District Council

"Horsham District Council Improved security, £30,000 saved in network management costs, and a protected hybrid workforce – thanks to next-gen firewalls. Over 800 users connect to the Council’s network at any time, either on-site or remotely, across a range of devices. Not only was legacy security architecture complex and clunky to manage, its depth of […]"

Wakefield Grammar School Foundation

"Wakefield Grammar School Foundation Successful 1:1, personalised digital learning for 2,000+ students across 3 schools, underpinned by next-gen wireless networking. The Foundation’s existing network was not able to provide the visibility or flexibility their IT teams required, to support future-focused learning, or ensuring secure, reliable connectivity. Transitioning to a future-proofed network has enabled the Foundation […]"

Jarrow School

"Jarrow School Jarrow School has future proofed its network and improved bandwidth performance by 500% following a switching project from Redway Networks Jarrow School’s exceptional facilities, including state-of-the-art classrooms, PC suites, and virtual learning environment, were being limited by legacy switches that impacted 800 students and 100 staff. Bandwidth requirements caused issues from edge to […]"

Brighton Hill Community School

"Brighton Hill Community School With a doubled number of students but a 10 year old wireless network, it’s no surprise that seamless connectivity, device capacity, and campus coverage were all falling short of supporting innovative learning. Building a thriving educational environment with easily adopted EdTech, rising devices and secure, seamless streaming demanded a Wi-Fi solution […]"

Mowbray Education Trust

"Mowbray Education Trust Mowbray Education Trust benefits from WiFi fault-finding surveys from Redway Networks With 400 teachers and 1,100 students spread across 7 schools, supporting connectivity that can support learning, teaching and monitoring at each site is a complex task for Mowbray Academy Trust’s IT department. Several schools were having trouble giving students access to […]"

Blackburn College

"Blackburn College selects Redway Networks for a WiFi Survey that paves the route to a new high-performance wireless network As one of the largest colleges in the UK – with over 750 staff and 10,000 students – Blackburn College’s wireless network has to support an increasingly huge number of users, devices and applications. With the […]"

Anord Mardix

"Anord Mardix Anord Mardix improves network capacity at UK sites with robust, scalable WiFi solution Anord Mardix, the world leader in electrical engineering and manufacturing, has improved wireless network performance at 3 of its UK production facilities with a high-performance WiFi solution from WiFi experts Redway Networks. The new Cambium cloud-networking platform provides seamless, hyper-fast […]"

Selby College

"Selby College improves the student experience with high-density WiFi 6 – delivered in just 8 weeks – from Redway Networks. Thanks to a new hyper-secure, robust networking solution, the digital experience of students and staff now matches the campus’ state-of-the-art facilities which have made the College one of the most up-to-date education providers in the […]"

Liverpool & London Music Academy

"Liverpool & London Music Academy improves access to digital teaching and learning with Cisco Meraki cloud-based networking solution Following a surge in student applications alongside an expansion across two new state-of-the-art campuses in Liverpool and also in London, LMA – co-owned by global superstar Robbie Williams – has invested in a high-performance wireless solution to […]"

John Warner School

"John Warner School Cloud-based Wi-Fi 6 future-proofs scalability, coverage and security with 11 year licence The transition to Cisco Meraki has given the school a hyper-secure wireless network that delivers faster speeds and more capacity for its high-density environment, with intuitive cloud-based network performance monitoring.   The new WiFi solution has delivered: A network that […]"

Hollybank Trust

"Hollybank Trust Improves Learning for SEN Students & Teachers with Lenovo PCs from Redway Networks Hollybank Trust educates over a hundred PMLD children and adults in West Yorkshire, across its school, residential homes, and adult daytime activity centre, which includes a state-of-the-art therapy centre, assistive technology suite and several sensory rooms. Following investment in SEN […]"

St Augustine’s RC High School

"St Augustine’s RC High School Classrooms ready for emerging EdTech for 11 years with Wi-Fi 6 solution from Redway Networks. As one of the largest Catholic schools in Lancashire, St Augustine’s teachers see EdTech and digital resources as a core component of classroom engagement. Investing in a future-ready wireless solution has freed up educators and […]"

Sir Henry Floyd Grammar School

"Sir Henry Floyd Grammar School Seamless connectivity for digital media across 3,000 devices, delivered through Wi-Fi 6 technology. Sir Henry Floyd Grammar School – part of the Insignis Academy Trust – has safeguarded high performance wireless into the future thanks to the latest ExtremeCloud IQ WiFi 6 solution, offering superior connectivity as well as agile, […]"

Erasmus Darwin Academy

"Erasmus Darwin Academy Improved connectivity and network controls supports safe, seamless access to apps, resources and collaborative tools. The new wireless solution has given the school a robust network capable of managing and controlling its scaling number of connected devices – including BYOD – with uninterrupted access to its student management information system.   The […]"

Pets Corner

"Pets Corner Pets Corner supports warehousing operations in its new distribution services warehouse with high-performance WiFi from Redway Networks. The UK’s leading ethical pet retailer has implemented a fast, reliable enterprise wireless solution from Redway Networks in its newly constructed warehouse in Handcross, West Sussex. The new wireless solution provides reliable connectivity that supports its […]"

Fladgate LLP

"Our new wireless solution from Redway Networks provides fast speeds, improved capacity, better coverage and the highest levels of security and control."

Uckfield Town Council

"Our new wireless solution has been a massive leap for the town council and I can now look at future projects. Redway Networks has given me the best service I’ve ever received from an IT company and its wireless expertise, product knowledge and service are first-class."

WF Education Group Ltd

"Very, very impressed with Redway Networks. The team were always on hand to provide assistance and everything promised was delivered"

Blue Coat School

"Although we are a new client of Redway Networks, the level of service and support we have experienced are first class. We have taken delivery of a small number of Aerohive products which have thoroughly impressed us here. Coupled with the great service at Redway Networks we intend to carry out a full rollout to replace our current aging Juniper WiFi Solution. We look forward to a long and fruitful relationship with Redway Networks"

Ryvers School

"Aerohive Wireless works seamlessly and having visibility of the data via the HiveManager NG portal is a real bonus. The services provided by Redway Networks throughout the implementation was impeccable."

Great Bridge School

MK Hospital

Northumberland

Lincoln NHS

The University of Buckingham

Salisbury NHS

South Essex College

Boston College

College Of North West London

Worcester City Council

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Extreme Partnership wireless mobility

Privacy Overview

1. Introduction

The increasing popularity of mobile terminals equipped with wireless local area network (LAN) functions has driven the installation of wireless LAN access points (APs) in both indoor and outdoor locations and the creation of Internet connection environments in all sorts of places. In line with this trend, NTT EAST has made its 5th-generation home gateway compliant with the new IEEE802.11ac *1 wireless networking standard and has been expanding its communication services using wireless LAN such as by launching FLET’S HIKARI (optical broadband) services capable of gigabit-class communications. Services in a variety of formats are also expanding such as Wi-Fi *2 access for apartment buildings and Wi-Fi access for corporate use.

However, communication faults can occur as a result of insufficient signal strength, signal interference, incompatible communication protocols, and other factors. Finding ways of recovering from faults quickly and improving service quality has consequently become a matter of urgency.

In this article, we introduce recent case studies of wireless LAN problems handled by the Technical Assistance and Support Center.

2. Case study 1: Wi-Fi access for an apartment building

In this section, we describe a problem a customer had with Wi-Fi access for an apartment building and explain how it was rectified.

2.1 Overview and report

Wi-Fi access for apartment buildings is an Internet connection service via wireless LAN targeting a building of 4 to 12 units. In this service, any room in the building should be able to connect to wireless LAN via radio signals transmitted from shared APs installed outdoors. In this case study, a report was received that an AP connection could not be made from an indoor location, so an investigation was carried out.

2.2 Results of investigation and causes of fault

We considered the possibility that the signal strength of wireless LAN was insufficient, so we checked the manner in which the antennas were installed. We found some cases in which antennas were installed at a height midway between the first and second floors or on the ceilings of balconies, as shown in Fig. 1 , and we surmised that the signals in such cases were not strong enough to reach indoors. The indoor signal-strength distribution measured with a wireless LAN tester [1] (a product developed by the Technical Assistance and Support Center and awarded a 2016 NTT EAST President’s Commendation) is shown in Fig. 2 . It was found that the signal strength in the living room where the customer was using wireless LAN was –76 dBm, which we considered to be insufficient.

Furthermore, considering that wireless LAN channel interference might be occurring, we measured the channel interference with the wireless LAN tester and found that channels 9 and 11 were indeed interfering with each other as shown in Fig. 3 .

We surmised that the causes of the fault were insufficient indoor signal strength due to an inappropriate antenna installation format and interference of wireless LAN signals due to inappropriate channel allocation to the AP.

2.3 Proposed method

Since radio signals are more able to permeate through windows than walls, installing an antenna on the balcony side rather than the entrance side of a unit would make it easier for indoor terminals to receive signals. Signals from a Wi-Fi antenna are strongly transmitted in the direction perpendicular to the antenna direction as shown in Fig. 4 . To therefore transmit radio signals efficiently into a room, the antenna should be vertically installed at a height aligned with the center of the window frame. Moreover, installing the antenna away from walls can secure a line-of-sight toward rooms, thereby achieving more efficient transmission of radio signals into rooms, as shown in Fig. 5 .

Therefore, an optimal antenna installation format would be the one shown in Fig. 6 . That is, the antenna should be vertically installed at a height corresponding to the center of the window and at a distance from the wall. The indoor signal-strength distribution after changing the antenna installation format is shown in Fig. 7 . The signal strength in the living room was now –61 dBm, reflecting a 15 dB improvement compared with that before antenna relocation.

Finally, allocating wireless LAN channels 1, 6, and 11 as shown in Fig. 8 can prevent the occurrence of interference.

3. Case study 2: Wi-Fi access service for corporate use

The second case study involved a problem a customer had with Wi-Fi access for corporate use. We describe the problem and the countermeasure in this section.

3.1 Overview and report

Wi-Fi access for corporate use is an Internet connection service via wireless LAN targeting corporate customers. This service delivers AP units to the customer, who then installs them at various indoor locations. There were four AP units (one per room) installed in the customer’s office with each AP connected to a router, ONU (optical network unit), and PBX (private branch exchange), as shown in Fig. 9 . 90 smartphones that could connect to these APs had been used. The customer reported that disconnections occurred.

3.2 Results of investigation and causes of fault

We used a spectrum analyzer to measure the radio-signal condition in both the 2.4-GHz and 5-GHz bands in a room where disconnections had occurred. The results of these measurements are shown in Fig. 10 . Other than Wi-Fi signals, no interfering signals could be observed.

Next, using AirMagnet (a generally available wireless LAN analysis tool), we measured the protocol on the radio signal in a room where disconnections had occurred. The results are shown in Fig. 11 . These results revealed that no Block Ack message (acknowledgment that data were received) was returned from the terminal after a data transmission from the AP when a disconnection had occurred (using smartphone A), which resulted in the resending of Block Ack Request messages from the AP. To troubleshoot this result, we used smartphone B and found that the protocol had no problem in the order of data→Block Ack→data and so on.

We therefore surmised that the cause of the disconnection when using smartphone A was that Block Ack messages that should have been transmitted in reply to data packets from the AP were somehow missing.

3.3 Proposal to the customer

We confirmed that smartphone A was outside the scope of this system’s operational guarantee, so we proposed to the customer that smartphone A be replaced with a smartphone unit for which normal operation was guaranteed.

4. Case study 3: Home gateway (HGW) equipped with a wireless LAN function

The final case study involves a problem that occurred in a HGW.

4.1 Overview and report

A customer using a tablet terminal and a HGW equipped with a wireless LAN function reported that an application download would stop 2 to 3 seconds after starting.

4.2 Results of investigation and causes of fault

We measured the signal strength, channel interference, and interfering signals with a wireless LAN tester in the room, but found that no signal attenuation, channel interference, and interfering signals could be observed at the time of the fault.

We then measured the protocol for the radio signals. A download would normally be completed in the order of RTS (Request To Send)→CTS (Clear to Send)→data→Ack (acknowledgment that data were received), as shown in Fig. 12 . However, at the time of the fault, the AP would resend RTS repeatedly, while no CTS would be returned from the terminal.

We surmised from these results that the non-return of the CTS message from the terminal to the AP caused the AP to repeatedly resend RTS messages, thereby stopping data transmission from the HGW and bringing the download to a halt.

4.3 Countermeasure

We checked the operating system (OS) of the tablet terminal and found that it was an old version. We therefore updated the OS to the latest version, and confirmed that a download was completed.

5. Conclusion

In this article, we introduced recent case studies of wireless LAN problems handled by the Technical Assistance and Support Center. With the proliferation of various types of wireless LAN services, the causes of faults in these services are becoming increasingly diverse. The EMC Engineering Group of the Technical Assistance and Support Center endeavors to achieve prompt resolution of faults related to wireless LAN and to contribute to the smooth provision of communication services. To this end, it is actively engaged in technology dissemination activities through technical support, development, and technical seminars.

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Case Study of Wireless Networking for Small Business

2014, International Journal of Engineering

Mobile and wireless networks have undergone rapid changes and have seen an unprecedented growth during the last few years. Traditional ways of networking have changed to accommodate new lifestyles and newer ways of working. Wireless networks offer several advantages over fixed or wired networks through mobility, flexibility, ease of access, speed of deployment, and low cost. Flexibility of wireless networks facilitates rapid deployment. Finally, this paper identifies the benefits of wireless technology for small businesses and features of wireless networks. Keywords—Wireless Networking, Wireless Technology, Benefits & Features of Wireless Networks.

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Next-Generation Wi-Fi Networks with Generative AI: Design and Insights

• Wang, Jingyu
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Generative artificial intelligence (GAI), known for its powerful capabilities in image and text processing, also holds significant promise for the design and performance enhancement of future wireless networks. In this article, we explore the transformative potential of GAI in next-generation Wi-Fi networks, exploiting its advanced capabilities to address key challenges and improve overall network performance. We begin by reviewing the development of major Wi-Fi generations and illustrating the challenges that future Wi-Fi networks may encounter. We then introduce typical GAI models and detail their potential capabilities in Wi-Fi network optimization, performance enhancement, and other applications. Furthermore, we present a case study wherein we propose a retrieval-augmented LLM (RA-LLM)-enabled Wi-Fi design framework that aids in problem formulation, which is subsequently solved using a generative diffusion model (GDM)-based deep reinforcement learning (DRL) framework to optimize various network parameters. Numerical results demonstrate the effectiveness of our proposed algorithm in high-density deployment scenarios. Finally, we provide some potential future research directions for GAI-assisted Wi-Fi networks.

• Computer Science - Networking and Internet Architecture

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• Published: 15 August 2024

Financial network communities and methodological insights: a case study for Borsa Istanbul Sustainability Index

• Larissa M. Batrancea 1 ,
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Humanities and Social Sciences Communications volume  11 , Article number:  1046 ( 2024 ) Cite this article

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• Complex networks
• Operational research

This study investigates the influence of Environmental, Social, and Governance (ESG) scores on the clustering and community formation of companies within various network models. Using daily closing prices of 78 companies operating in the Borsa Istanbul Sustainability Index, we constructed correlation, mutual information (both continuous and discrete), and causality (both linear and nonlinear) networks to analyse intercompany relationships. We performed community detection using the Leading Eigenvector and Girvan–Newman methods, which revealed that companies within the same sector, particularly in the financial and manufacturing sectors, tend to form tight-knit communities. These intra-sectoral clusters reflect strong market behaviour correlations driven by sector-specific factors. Additionally, mixed-sector communities highlighted the presence of significant inter-sector dependencies. To assess the impact of ESG scores on these communities, nonparametric tests such as the Kruskal–Wallis, Conover, and log-rank were applied. Results showed that specific ESG factors, including emission, CSR strategy, innovation, and human rights, significantly influenced community formation. For instance, companies with strong performance in emission reduction and CSR strategies were found to form more cohesive communities, emphasizing the role of sustainability in shaping financial networks. Study findings underscore the critical role of ESG factors in financial market dynamics, promoting sustainable investment practices by highlighting the importance of integrating ESG considerations into investment decisions. These results suggest that sustainability metrics not only affect individual company performance but also contribute to the formation of interconnected communities with shared sustainability practices.

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Introduction.

Understanding market dynamics requires a deep knowledge of financial networks, which offer a comprehensive and detailed view of the relationships and interactions between various market entities such as stocks, industries, and organizations. We construct these networks by discovering and evaluating the connections between different financial instruments and entities using measures such as price correlations, trade volumes, and other relevant financial data. By undertaking this action, they reveal the market structure and provide significant insight into the interplay between different factors (Chi et al., 2010 , Guo et al., 2018 , Karpman et al., 2023 , Shirokikh et al., 2022 ).

Through the analysis of financial networks, researchers and analysts can identify patterns of connectivity that are not immediately apparent from raw data alone. For example, they can detect clusters of highly interconnected stocks that tend to move together, known as communities or modules, which often correspond to specific sectors or industries. These clusters can highlight sectoral interdependencies and information flow within and between different parts of the market (Raddant and Kenett, 2021 , Pazitka et al., 2021 , Upadhyay et al., 2020 ). Additionally, financial networks can reveal key nodes or hubs, which are entities with a high degree of connectivity that play a significant role in the overall stability and functionality of the market. Identifying these influential nodes is crucial for understanding systemic risk and potential points of vulnerability within the financial system.

The analysis of financial networks also enables the study of information flow and influence among market participants. By examining how information or shocks propagate through the network, analysts can gain insights into the mechanisms of market reactions and the spread of financial contagion. This understanding is critical for predicting market behaviours, as it allows for the anticipation of how different parts of the market may respond to various stimuli, such as economic news, policy changes, and geopolitical events.

In recent years, Environmental, Social, and Governance (ESG) factors have emerged as vital considerations in financial decision-making. ESG factors encompass a wide range of criteria that assess a company’s performance beyond traditional financial metrics. Environmental factors include a company’s impact on the environment, such as carbon emissions and resource usage. Social factors evaluate how a company manages relationships with employees, suppliers, customers, and the communities in which it operates. Governance factors examine a company’s leadership, executive pay, audits, internal controls, and shareholder rights.

The growing prominence of ESG factors in financial analysis reflects a broader shift towards sustainable and responsible investing. Investors are increasingly aware that companies with strong ESG performance are better positioned to manage risks, capitalize on opportunities, and achieve long-term financial success. Studies have shown that integrating ESG metrics into financial analysis can lead to more resilient investment portfolios (Ma 2023 , Naffa and Fain 2020 ). Companies with high ESG ratings tend to have lower volatility, higher profitability, and better long-term returns compared to their peers with poor ESG performance. Moreover, the integration of ESG metrics is recognized for promoting sustainable investment practices. By considering ESG factors, investors can identify companies that are committed to sustainability and ethical practices, which can lead to positive social and environmental outcomes. This approach not only aligns with the growing demand for corporate responsibility but also enhances the resilience of financial markets. Sustainable investment practices can help mitigate risks associated with environmental degradation, social unrest, and poor governance, thereby contributing to the stability and health of the financial system.

Despite the extensive research on financial networks, there remains a significant gap in understanding how ESG factors influence the formation and dynamics of networks. Traditional financial network studies primarily focus on metrics such as price correlations, trading volumes, and return dependencies to analyse market structures and predict behaviours. While these studies provide valuable insights into the interconnectedness and risk propagation within financial markets, they often overlook the integration of ESG metrics, which can offer a more comprehensive understanding of market dynamics.

Existing studies frequently miss the critical role that ESG factors play in shaping the relationships between market entities. ESG metrics encompass a range of non-financial factors that reflect a company’s long-term sustainability and ethical practices, such as carbon footprint, labour practices, board diversity, and transparency. By excluding these factors, current research may fail to capture the full spectrum of influences that drive market behaviours and interdependencies. For instance, companies with strong environmental practices might be more interconnected due to shared sustainability goals, leading to distinct community structures that are not apparent when only financial data are considered.

The integration of ESG metrics into financial network analysis can provide insights into how sustainability practices affect market interconnectivity and community structures. Companies that prioritize ESG criteria may exhibit different connectivity patterns, forming clusters based on shared environmental initiatives, social responsibilities, or governance standards. This can reveal hidden dependencies and relationships that traditional financial metrics might miss, such as the tendency for companies with robust ESG practices to be more resilient during economic downturns or crises due to better risk management and ethical governance. Furthermore, understanding the impact of ESG factors on financial networks can enhance the predictive power of these models. Incorporating ESG metrics can help identify systemic risks and opportunities that are not evident through financial data alone. For example, a network analysis that includes ESG factors might reveal that companies with poor environmental practices are more susceptible to regulatory changes or public backlash, leading to greater market volatility and risk of contagion. Additionally, the integration of ESG metrics into financial network analysis can inform more sustainable investment strategies. Investors increasingly seek to align their portfolios with ethical and sustainable practices, and understanding the role of ESG factors in financial networks can guide them in identifying companies and sectors that are not only financially robust but also committed to long-term sustainability. This can lead to more informed investment decisions that support both financial returns and positive societal impacts.

This study aims to bridge the gap in existing research by investigating the impact of ESG scores on clustering and community formation within various financial network models. The primary objective is to integrate sustainability metrics into the analysis of financial networks to provide a more comprehensive understanding of market dynamics. By incorporating ESG factors, the study seeks to uncover how environmental, social, and governance considerations influence intercompany relationships and the formation of distinct communities within these networks.

To achieve this, the study employs several sophisticated network models, each offering a unique perspective on intercompany relationships. First, correlation network models will be utilized to identify how company stock prices move in relation to one another. In these models, edges represent the degree of correlation between the daily closing prices of different companies, with higher correlations indicating stronger connectivity. This approach will help detect sectoral clusters where companies within the same sector, such as finance or manufacturing, exhibit similar stock price movements due to shared economic factors.

Subsequently, the study will utilize mutual information network models to collect and analyse both linear and nonlinear connections among stock values of different companies. By employing both continuous and discrete mutual information, these networks will surpass basic linear correlations to uncover intricate interdependencies and information exchanges among organizations. This approach seeks to reveal insights into the impact of information flow and common market behaviours on community structures, potentially showing important inter-sectoral linkages. Furthermore, causality network models will be utilized to comprehend the directional effects among stock values of different organizations. These models will illustrate how fluctuations in the stock price of one firm can forecast those of another firm, thus capturing the cause-and-effect interactions within the market. We will conduct both linear and nonlinear causality analyses to obtain a full understanding of these interdependencies.

To assess the influence of ESG metrics on community structures, the study will employ nonparametric tests, including the Kruskal–Wallis, Conover, and log-rank tests. These tests are particularly suitable for this analysis as they do not assume a specific distribution for the data, making them robust tools for evaluating relationships between ESG scores and community formation.

Through this multifaceted approach, the study aims to provide valuable insights into the role of ESG factors in shaping financial networks. By understanding how sustainability metrics influence market connectivity and community structures, the findings of this study can inform more sustainable investment practices and contribute to the development of resilient and responsible financial markets.

Study findings reveal distinct patterns of interconnectivity among companies across different network models. Correlation networks highlight strong sectoral linkages, particularly within the finance and manufacturing sectors. Mutual information networks provide insights into both intra- and inter-sector dependencies, while causality networks demonstrate predictive relationships in stock price movements. The nonparametric test results indicate that ESG factors such as Emission, CSR Strategy, Innovation, and Human Rights significantly influence community formation, suggesting that companies with strong performance in these areas tend to form more cohesive communities.

The remainder of this paper unfolds as follows: section “Literature review” embarks on a comprehensive literature review, laying the groundwork for our study. Section “Methodology” delves into the methodology, detailing the construction of network models and the application of community detection methods. In the section “Results”, we introduce the dataset and provide an in-depth analysis of the influence of ESG sub-scores on overall ESG performance. This section then transitions into a detailed presentation and discussion of network and community results. Section “Discussions” explores the nonparametric tests employed to evaluate the impact of ESG scores, offering a detailed analysis of findings. Finally, the section “Conclusions” ends the study with a summary of key insights and thoughtful suggestions for future research directions.

By integrating ESG factors into financial network analysis, this study not only enhances understanding of market dynamics but also promotes sustainable investment practices. The insights gained from this research can guide investors and policymakers in fostering more resilient and socially responsible financial markets.

Literature review

Understanding the role of Environmental, Social, and Governance (ESG) factors in financial networks is essential for grasping the complexities of market dynamics and sustainable investment practices. This literature review synthesizes insights from recent studies on the integration and impact of ESG metrics within financial networks.

Kim and Li ( 2021 ) explored the relationship between ESG factors and corporate financial performance, showing that higher ESG scores were linked to increased profitability and better credit ratings, particularly in large firms and those with strong governance practices. Similarly, Sinha et al. ( 2019 ) conducted a meta-analysis of 100 studies, confirming that ESG integration generally led to improved financial performance across different geographic domains. Aybars et al. ( 2019 ) demonstrated a significant positive relationship between ESG scores and return on assets for S&P 500 firms, highlighting the importance of ESG factors in enhancing operational performance. Additionally, Caporale et al. ( 2022 ) analysed the impact of ESG factors on financial performance and found that ESG scores significantly enhanced financial stability and resilience against market shocks. Luo et al. ( 2024 ) examined the integration of ESG metrics into portfolio management and found that ESG-oriented portfolios outperformed traditional ones, particularly in volatile markets.

Batrancea et al. ( 2022c ) highlighted the importance of governance quality and social policies in fostering economic growth, with a limited focus on environmental sustainability. Financial performance was measured through GDP growth, investment rates, and industrial production, showing the positive impact of good governance and social policies. Batrancea et al. ( 2022a ) integrated ESG factors by examining environmental policies, social welfare, and governance quality, showing their positive influence on economic growth. Financial performance indicators such as GDP growth, productivity, and investment demonstrated that robust ESG frameworks supported sustainable economic growth. Similarly, the study by Batrancea et al. ( 2022b ) examined the role of SME financing, indirectly addressing environmental and social impacts, with a strong focus on governance and regulatory environments. It concluded that well-financed SMEs significantly contributed to economic growth and stability, as measured by GDP and productivity metrics. The analysis from Batrancea et al. ( 2021 ) emphasized the importance of governance quality and social infrastructure in driving economic growth, with some consideration of environmental sustainability. Financial performance was evaluated through GDP growth and investment flows, showing that better governance and social infrastructure were crucial for sustainable growth. Additionally, Batrancea et al. ( 2023b ) discussed the impact of environmental regulations, social factors, and governance quality on economic growth over the past fifty years. It found that countries with strong ESG frameworks experienced more robust economic growth, measured by GDP, investment, productivity. Batrancea ( 2022 ) focused on the role of SMEs in economic growth, considering environmental sustainability, social equity, and supportive governance. Financial performance was assessed through SME growth rates and GDP, concluding that supportive policies were essential for SME-driven economic sustainability. Finally, Batrancea et al. ( 2023a ) highlighted the positive impact of investments in wellbeing-related infrastructure, such as healthcare and education, on regional economic growth. Financial performance was measured through regional GDP growth and productivity, showing that better social infrastructure determined higher economic growth.

ESG integration in investment strategies involves incorporating environmental, social, and governance factors into investment decisions to enhance long-term financial returns and sustainability. Chan et al. ( 2020 ) showed that incorporating ESG signals into factor-based investing strategies could yield similar historical performance to traditional factor portfolios, suggesting that ESG metrics might enhance financial value and quality factors. Zaccone and Pedrini ( 2020 ) found that private equity firms were increasingly integrating ESG factors into their investment strategies, primarily for risk management and value creation, though challenges in measuring ESG issues persisted. Ma ( 2023 ) discussed international trends in ESG integration, emphasizing the link between ESG ratings and company performance, and suggesting that ESG considerations provided a more comprehensive dimension for investment decision-making. Park and Lee ( 2023 ) highlighted the growing importance of ESG factors in investment strategies, showing that ESG integration generated improved risk-adjusted returns. Park and Oh ( 2022 ) explored how ESG factors influenced investment decisions and found that ESG considerations significantly enhanced portfolio resilience.

ESG factors play a critical role in promoting financial stability by mitigating environmental, social, and governance risks that can impact economic systems. Incorporating ESG considerations into financial decision-making can enhance the resilience and sustainability of financial markets, leading to more stable and predictable economic outcomes. Stolbov and Shchepeleva ( 2022 ) reviewed empirical studies on the impact of ESG factors on financial stability, finding that higher ESG rankings enhanced stability by mitigating individual and systemic risks. Lupu et al. ( 2022 ) examined the impact of ESG scores on European financial stability, using advanced methods to uncover dependencies not evident in average distribution levels. Ling et al. ( 2023 ) found that higher ESG scores determined increased financial stability and reduced systemic risk, particularly in the banking sector.

Integrating ESG factors into business practices can significantly enhance a company’s market value by attracting socially responsible investors and improving long-term financial performance. Companies with strong ESG performance often enjoy higher valuations and better access to capital, as they are perceived to be more sustainable and less risky. Ionescu et al. ( 2019 ) investigated the relationship between ESG factors and market value in the travel and tourism industry, finding that good governance scores significantly influenced market value regardless of geographic region. Lee and Isa ( 2023 ) explored the impact of ESG factors on financial performance in Malaysia, showing that environmental factors positively influenced ROE, while social and governance factors impacted long-term market performance. Yoon et al. ( 2024 ) found that companies with high ESG ratings had higher market values and better financial performance. Furthermore, Junius et al. ( 2020 ) reported no significant direct impact of ESG scores on firm performance and market value in ASEAN countries, suggesting that ESG factors were not fully integrated into performance metrics in these regions.

In recent years, the intersection of financial performance and sustainability practices has garnered significant attention, particularly within the context of emerging markets such as Turkey. Current studies have explored various dimensions of this relationship, providing a nuanced understanding of how ESG factors impact financial markets and corporate behaviour in Borsa, Istanbul. For instance, the relationship between monetary policy and financial asset returns in Turkey has been investigated using time, frequency, and quantile-based effects, highlighting the intricate dynamics between macroeconomic policies and market performance by Kartal et al. ( 2024b ). Additionally, research by Kartal et al. ( 2024a ) modelled the link between environmental, social, and governance disclosures and scores, focusing on publicly traded companies in the Borsa Istanbul Sustainability Index. This study underscores the importance of transparent ESG disclosures in shaping investor perceptions and corporate valuations. Furthermore, the influence of climate risk, carbon allowances, and technological factors on the ESG market has been assessed within the European Union context, providing comparative insights that are relevant for understanding similar dynamics in Turkey by Pata et al. ( 2024 ). These studies collectively emphasize the critical role of ESG factors in financial analysis and emphasize the need for integrating sustainability metrics to foster more responsible financial markets.

ESG metrics provide valuable data for predictive analysis, allowing investors and analysts to forecast financial performance and risks more accurately. By integrating ESG metrics into predictive models, businesses can identify potential opportunities and threats, leading to more informed and strategic decision-making. Ang et al. ( 2023 ) utilized dynamic intercompany relationships to predict ESG ratings, demonstrating a significant improvement in prediction performance when incorporating network information. Giese et al. ( 2019 ) linked ESG information to company valuation and performance through cash flow and risk channels, suggesting that ESG characteristics could be useful financial indicators. Lee et al. ( 2024 ) analysed how ESG factors predicted stock market movements. Gong et al. ( 2024 ) reported that ESG factors significantly enhanced the predictive power of financial models for investment decisions.

Methodological approaches in ESG research integrate quantitative and qualitative metrics, with future directions focused on developing sophisticated predictive models. Meiden and Silaban ( 2023 ) emphasized the need for comprehensive and standardized metrics to effectively capture and compare environmental performance within the broader ESG framework, recognizing the interdependencies between these dimensions. Similarly, Escrig-Olmedo et al. ( 2017 ) proposed a fuzzy multicriteria decision-making approach to integrate the preferences of diverse ESG investors, highlighting the importance of sector-specific metrics. Empirical research by Efimova et al. ( 2021 ) demonstrated a positive relationship between ESG commitment and market returns, suggesting that ESG factors could be significant drivers of financial performance. Furthermore, Raza et al. ( 2022 ) developed machine learning algorithms to predict ESG scores based on financial data, advocating for the use of artificial intelligence to enhance the accuracy and relevance of ESG evaluations. Zhang and Zhang ( 2023 ) also reviewed the application of machine learning in ESG research, noting its potential to address challenges in ESG disclosure and improve the reliability of ESG ratings. These studies collectively emphasize the growing trend toward integrating sophisticated predictive models and machine learning techniques in ESG research to enhance the precision and applicability of ESG assessments.

The integration of ESG factors into financial network analysis provides valuable insights into market dynamics and promotes sustainable investment practices. By incorporating ESG metrics, researchers can enhance the predictive power of financial models, identify systemic risks, and support the development of resilient financial systems.

Methodology

Utilizing mathematical principles, particularly those derived from graph theory, enhances our understanding of complex interrelated systems. In these networks, nodes represent discrete items (such as stocks or bonds), while edges indicate the connections or affiliations between them. Mathematically, a graph is a tuple \(G=(V,E)\) , where V represents the set of nodes (or vertices) and \(E\subseteq V\times V\) represents the set of edges. Weight functions \(\omega :E\to {{\mathbb{R}}}^{+}\) are often used to assign weights to edges in real-world scenarios, such as the financial network of the Borsa Istanbul Sustainability Index. This generates the formation of a weighted graph, represented as \(G=(V,E,\omega )\) .

This study examines five distinct approaches to network creation, each establishing the relationship between nodes that represent companies through different methods for generating edges. Weighted financial networks are constructed by assigning weights to the edges based on the selected approach. The primary objective of the study is to examine the clusters in financial networks derived from various methodologies, specifically focusing on graph communities.

Correlation networks

Within the complex realm of global economics, the interconnection of financial networks plays a crucial role in shaping market directions and impacting economic stability. Financial networks, composed of intricate systems of institutions, markets, and tools, are essential in facilitating the movement and distribution of capital globally. The interconnectedness of these networks fosters a dynamic ecosystem where economic activity, investments, and regulations are tightly connected. Understanding the interconnections within financial networks is vital for effectively navigating the complexities of contemporary finance, as it impacts not only individual institutions but also has extensive ramifications for entire economies and societies.

In financial correlation networks, each node represents a financial asset, and the edge weights measure the correlation between the returns of connected assets. To analyse the logarithmic return of the daily closing price of stocks, we use the following formula:

This equation calculates the difference in the daily closing price of stock i at time t .

To compute the Pearson correlation coefficient between stocks i and j , we use the following formula:

where \(\langle \cdot \rangle\) represents the temporal average. The Pearson correlation coefficient is a commonly used statistical measure in finance that quantifies the extent of the linear relationship between two financial time series. A coefficient close to 1 indicates a strong positive correlation, suggesting that the two time series consistently move together. Conversely, a coefficient close to −1 indicates a significant negative correlation, where the variables move in opposite directions. A correlation value close to zero indicates a minor or insignificant correlation, meaning there is no noticeable linear relationship between time series.

The weight function derived from the correlation coefficient is given by

By starting with a comprehensive initial network setup, where each node is intricately connected and assigned weights based on correlation distance, we uncover detailed patterns of relationship dynamics. Notably, as correlations strengthen, either positively or negatively, the corresponding edge weights tend to decrease towards zero, indicating stronger linkages. Conversely, weaker correlations result in weights approaching \(\sqrt{2}\) . In this framework, weights serve as quantifiable measures of relationship intensity, with smaller values indicating stronger links.

Since this approach creates a connection, albeit weak, between every node, the resulting network is mathematically equivalent to a complete graph. To mitigate the impact of insignificant connections on the analysis, filtering techniques are employed to enhance the realism of models by removing weak edges. This study utilizes the triangulated maximally filtered graph (TMFG) filtering approach, known for its effectiveness in financial networks (Akgüller, 2019 ; Balcı et al., 2022 ; Millington, 2022 ; Turiel et al., 2022 ).

TMFGs provide a robust analytical framework for financial networks, methodically extracting important information from complex interconnected systems. In financial networks, TMFGs often begin with a comprehensive network structure where nodes represent different financial firms and edges indicate connections between them. Edges are weighted according to correlation distances, reflecting the intensity of relationships. The triangulation process involves identifying cycles and closing triangles within the network, thereby improving the representation of interdependencies among financial institutions. The TMFG method imposes a structural constraint that limits the inclusion of zero-order correlations to a maximum of 3| V |−6, where | V | represents the number of nodes. The TMFG process starts by selecting four nodes with the highest cumulative correlations to all other nodes. It then systematically adds each node with the highest total of three correlations to the existing network until all nodes are included. For more details, readers are referred to Massara et al. ( 2016 ).

The topologically triangulated structure used throughout this paper is denoted as \({G}_{F}=(V,{E}_{F},\omega )\) , where \({E}_{F}\subset E\) represents the filtered edge set. Implementing this triangulated framework allows for a more detailed understanding of systemic risk and interconnections. By using weighted edges derived from correlation distances, filtering techniques are applied to enhance the network, emphasizing important interactions and reducing the impact of noise.

Mutual information networks

Within the domain of financial systems, the concept of mutual information has become a vital framework for understanding the complex connections and interrelationships within networks. Mutual information in financial networks quantifies the degree to which the actions or performances of one entity provide insights into those of another, revealing the shared information and interconnections among various financial elements. Studying mutual information is crucial for understanding the dynamics that drive market movements, risk transmission, and systemic stability in today’s interconnected and complex financial environments. This quantitative metric provides valuable insights into the flow and sharing of information among different entities in the financial ecosystem, helping one to grasp the relationships that shape the modern financial landscape.

This study constructs a weighted network by using mutual information associations among time series derived from logarithmic returns of closing prices given in Eq. ( 1 ). The use of continuous and discrete bivariate mutual information methodologies allows for the capturing of distinct dynamics.

Calculating continuous mutual information is essential for uncovering the connections between logarithmic returns of closing prices in financial networks. This process involves accurately calculating the continuous mutual information between pairs of organizations, offering a quantitative assessment of how interconnected their return behaviours are. To initiate this calculation, logarithmic returns are treated as continuous stochastic variables, and their joint probability density function is computed using kernel density estimation techniques. The integral of the joint probability density function

quantifies the information that is mutually communicated between the logarithmic returns of two organizations, considering both linear and nonlinear connections. In Eq. ( 4 ), \(p(C{l}_{i},C{l}_{j})\) is the joint probability density function of the logarithmic returns, and \(p(C{l}_{i})\) and \(p(C{l}_{j})\) are the marginal probability density functions. This computation determines how much the returns of one company convey information about the returns of another by comparing the joint probability distribution to marginal distributions. The continuous mutual information values obtained provide a detailed understanding of the intensity and nature of the connections, informing further network analysis and offering valuable insights into the complex dynamics of financial systems. This method is particularly useful for capturing intricate interdependencies that may not be fully represented by linear correlation measures, providing a more comprehensive view of the underlying linkages within financial data (Khoojine et al., 2023 , Nicola et al., 2020 , Zhao et al., 2023 ).

Discrete bivariate mutual information is a crucial step in exploring financial networks, using a discrete representation of logarithmic returns to quantify the informational content between pairs of companies. Initially, the continuous logarithmic returns are discretized into a finite set of bins, allowing for the application of discrete mutual information theory. Using the formula

the computation involves summing over all possible combinations of discretized values, considering their joint and marginal probability mass functions. This method effectively captures the statistical dependencies between discrete logarithmic returns, accounting for both linear and nonlinear associations. The resulting bivariate mutual information values represent the amount of shared information between pairs of companies, revealing the strength and nature of their connections in the context of financial movements. This approach is instrumental in overcoming challenges associated with continuous data, allowing for a more manageable and interpretable analysis (Viegas et al., 2020 , Yadav et al., 2020 ).

The weight assignment schemes used in this study are \(\frac{1}{{I}_{{{c}}}\left(C{l}_{i}{;C}{l}_{j}\right)}\) and \(\frac{1}{{I}_{{{d}}}\left(C{l}_{i}{;C}{l}_{j}\right)}\) for the respective networks. Incorporating the inverses of continuous mutual information and discrete bivariate mutual information as edge weights represents an intriguing approach to constructing financial networks. When considering continuous mutual information, applying edge weights as the reciprocal of estimated mutual information values results in a proportional decrease in the strengths of linkages. Higher mutual information values, indicating stronger connections between financial institutions based on logarithmic returns, lead to lower reciprocal edge weights. This method amplifies weaker connections by assigning them higher weights, resulting in a network representation that emphasizes links that are less connected or less dependent. In the context of discrete bivariate mutual information, the dynamic weighting technique assigns higher weights to edges with lower mutual information values, indicating a focus on relationships with lower information content. This reciprocal weighting approach offers a distinct perspective by prioritizing edges representing less statistically significant relationships within discretized financial data. The TMFG approach is used as a filtering technique to acquire the sets of E F for both networks generated using continuous and discrete bivariate mutual information. It is important to note that in both scenarios, the reciprocals of information values are used to determine the appropriate edge weights for TMFG filtering.

Causality networks

The study of financial networks has progressed beyond traditional linear methods to include causality analysis, revealing complex connections among time series data. Researchers explore the dynamic relationships between the logarithmic returns of closing prices among different companies by analysing both linear and nonlinear causalities (Stavroglou et al., 2017 , 2020 ; Zuhud et al., 2022 ). Statistical approaches, such as the Granger causality test, help identify predictive connections between the historical returns of one company and another, indicating linear causality. Simultaneously, advanced approaches in nonlinear causality analysis provide a more detailed understanding of the complex relationships that may occur, surpassing the limitations of linear models. The resulting financial networks encompass not only direct effects but also intricate, nonlinear interdependencies, offering a comprehensive view of how the financial performances of organizations influence one another. This extensive investigation into linear and nonlinear causality in financial time series data forms a basis for better understanding the underlying dynamics.

Consider two time series \(C{l}_{i}\left(t\right)\) and \(C{l}_{j}\left(t\right)\) , representing the logarithmic returns of daily closing prices for two distinct companies in the stock market. The linear causality between these time series can be formally assessed through the Granger causality test. Let \(C{l}_{i}\left(t\right)\) and \(C{l}_{j}\left(t\right)\) be jointly modelled in a lagged vector autoregressive framework as follows:

Here, p represents the lag order, \({\alpha }_{1s}\) and \({\alpha }_{2s}\) are coefficients, and \({\epsilon }_{i}\) and \({\epsilon }_{j}\) are white noise error terms. The Granger causality test assesses whether past values of \(C{l}_{i}\left(t\right)\) provide significant information in predicting \(C{l}_{j}\left(t\right)\) beyond the information contained in the past values of \(C{l}_{j}\left(t\right)\) itself. Formally, the null hypothesis \({H}_{0}\) is that \(C{l}_{i}\left(t\right)\) does not Granger-cause \(C{l}_{j}\left(t\right)\) . The test involves comparing the F-statistic from the restricted model (excluding lagged values of \(C{l}_{i}\left(t\right)\) ) with the F-statistic from the unrestricted model (including lagged values of \(C{l}_{i}\left(t\right)\) ). Statistical significance in rejecting \({H}_{0}\) indicates the presence of linear causality from \(C{l}_{i}\left(t\right)\) to \(C{l}_{j}\left(t\right)\) , thereby providing insights into the directional influence of one company’s logarithmic returns on another in the stock market.

Advanced techniques, such as Transfer Entropy, are used to investigate the nonlinear causality between time series. Let us denote the entropies of \(C{l}_{i}\left(t\right)\) and \(C{l}_{j}(t)\) as \(H\left(C{l}_{i}\left(t\right)\right)\) and \(H\left(C{l}_{j}\left(t\right)\right)\) , respectively. The conditional entropy of \(C{l}_{i}\left(t\right)\) given \(C{l}_{j}\left(t\right)\) is represented as \(H(C{l}_{i}|C{l}_{j})\) . Transfer Entropy, represented as \({TE}(C{l}_{i}\to C{l}_{j})\) , measures the decrease in uncertainty regarding the future values of \(C{l}_{i}\left(t\right)\) when the previous values of \(C{l}_{j}\left(t\right)\) are considered, surpassing the predictive capability of \(C{l}_{i}\left(t\right)\) based solely on its own previous values. In a formal sense, the expression

represents the Transfer Entropy from \(C{l}_{i}\) to \(C{l}_{j}\) . Nonlinear causality is identified when the value of \({TE}(C{l}_{i}\to C{l}_{j})\) is significantly different from zero. This method identifies the specific direction in which information flows between the logarithmic returns of the two companies, offering valuable insights into nonlinear connections that extend beyond linear links identified by conventional Granger causality analysis. Understanding these nonlinear causal connections enhances the description of dynamic interactions in the stock market.

Assigning weights to edges in networks generated by linear and nonlinear causality analyses using p -values provides a statistical method to determine the importance and reliability of detected causal connections among time series. For linear causality networks, edges can be assigned weights based on the p -values derived from Granger causality tests. Smaller p -values indicate greater statistical significance, so edges associated with more significant causal relationships are assigned lower weights. This methodology ensures that the network represents only statistically robust and reliable causal relationships. Similarly, for networks resulting from nonlinear causality analysis, p -values obtained from tests such as those evaluating the significance of Transfer Entropy can be used to assign weights to edges. Smaller p-values in the context of nonlinear causality provide stronger evidence for the existence of meaningful causal links. By integrating p-values into the weighting of edges, these networks not only visually depict causal structure but also allow researchers to focus on the most statistically plausible connections, enhancing the reliability of insights derived from network analysis.

Incorporating p-values in the context of TMFG filtering is highly relevant and enhances the robustness and reliability of network representation. The TMFG filtration technique aims to identify the most crucial connections within a network by selecting edges based on their robustness and significance. p-values provide an inherent criterion for this objective, offering a statistical assessment of the reliability of identified causal connections. By assigning lower weights to edges associated with lower p-values, the TMFG filtration can be tailored to emphasize connections that are statistically significant. This approach ensures that the final graph captures the most significant information flow and highlights edges with a high level of confidence in their causal influence.

Network Communities

Graph communities, mathematically referred to as subsets of nodes within a graph that exhibit higher connectivity among themselves than with nodes outside the subset, are essential structures in network analysis. Let \(G=\left(V,\,{E}_{F},\,\omega \right)\) represent a weighted filtered graph. A weighted community is then a subset \(C\subseteq V\) where the total edge weight within the community is significantly higher than the expected total edge weight in a null model. Mathematically, for a given partition of nodes into weighted communities \({\mathcal{C}}=\left\{{C}_{1},{C}_{2},\ldots ,{C}_{k}\right\}\) , the modularity \({Q}_{w}\) for weighted graphs is often employed as an optimization metric. The weighted modularity is an extension of the modularity concept for unweighted graphs, considering the sum of edge weights within communities. Formally,

where \(w({C}_{i})\) is the total weight of edges within community \({C}_{i}\) , \({w}_{j}\) is the weight of edge j , and W is the total weight of all edges in the graph. Weighted graph communities offer a more nuanced understanding of network structures by capturing varying strengths of connections between nodes, which is particularly relevant in applications where the intensity or significance of relationships plays a crucial role.

Graph communities are crucial for understanding intricate dynamics in financial networks and provide deep insights into the underlying structure of the market (Ferretti 2023 , Torri & Giacometti 2023 ). The process of identifying and analysing graph communities offers a perspective to comprehend the interrelationships and interdependencies among publicly listed organizations. These communities consist of organizations that have comparable financial features, market behaviours, or sustainability practices. As a result, they exhibit patterns that contribute to the overall resilience of the market.

When evaluating various network formation principles, including correlation, mutual information, and causation in financial networks, graph communities are particularly useful in capturing intricate dynamics. Correlation-based networks can reveal the interdependence between enterprises in a certain economic domain by identifying communities that showcase sectors or industries with strongly associated stock price movements. Conversely, networks built on mutual information expose communities that exhibit substantial information exchange, suggesting clusters of enterprises that react similarly to market occurrences. Introducing causality in network creation adds complexity by revealing how one company’s financial performance causally affects another, providing better understanding of cause-and-effect interactions within the financial ecosystem.

Within the framework of the Borsa Istanbul Sustainability Index, graph communities play a crucial role in identifying groups of enterprises that not only share financial connections but also engage in similar sustainability practices. Companies in a certain community may have comparable environmental, social, and governance (ESG) values, which collectively contribute to the overall sustainability goals of the index. Examining these communities enables stakeholders to identify areas of proficiency, possible weaknesses, and prospects for enhancement in relation to sustainability performance.

Two distinct community detection algorithms are employed in this study, each based on the modularity metric provided in Eq. 9 .

The identification of graph communities based on the leading eigenvector of the modularity matrix involves a more detailed understanding of the spectral clustering process (Newman 2006 ). The modularity matrix B is defined as

where A is the adjacency matrix, \({d}_{i}\) and \({d}_{j}\) are the weighted degrees of nodes i and j , and m is the total edge weight in the graph. Normalizing B by dividing each entry by 2 m yields a symmetric matrix.

The spectral clustering procedure commences by calculating the eigenvectors and eigenvalues of the normalized modularity matrix. The dominant eigenvector, associated with the largest eigenvalue, is obtained. The components of this eigenvector are subsequently employed as coordinates for the nodes, thus mapping them onto a multi-dimensional space. Subsequently, a conventional clustering technique is employed to process these coordinates. Common options include k-means clustering or hierarchical clustering. The partition of nodes that emerges from this process creates separate communities within the graph. Nodes that are assigned to the same cluster demonstrate comparable patterns in their connection strengths. Mathematically, let \({{\boldsymbol{v}}}_{1}\) be the leading eigenvector corresponding to the largest eigenvalue \({\lambda }_{1}\) of the normalized modularity matrix. Form a matrix \({{\boldsymbol{V}}}_{1}\) by stacking the entries of \({{\boldsymbol{v}}}_{1}\) , and apply a clustering algorithm to the rows of \({{\boldsymbol{V}}}_{1}\) This clustering process reveals graph communities based on the spectral properties of the modularity matrix.

The second approach we employ is founded on edge betweenness and is often known as the Girvan–Newman algorithm (Girvan & Newman 2002 ). Mathematically, the weighted betweenness centrality ( \(B(e)\) ) of an edge e in a weighted graph is computed as:

where \({g}_{{st}}(e)\) represents the number of shortest paths from node s to node t that traverse edge e , and \({g}_{{st}}\) is the total number of shortest paths from s to t . The weight of an edge is considered in these calculations.

The Girvan–Newman algorithm then proceeds by iteratively calculating the weighted betweenness centrality for all edges, identifying and removing the edge with the highest weighted betweenness. The process continues until the desired number of communities is reached or the graph becomes fully disconnected. Mathematically, let \({E}_{k}\) represent the set of edges removed during k iterations, and \({G}_{k}=\left(V,{E}_{k},{W}_{k}\right)\) be the graph after k iterations, where \({W}_{k}\) is the updated weight matrix. The iterative removal of edges partitions the graph into disjoint components, each representing a community. The modularity is used as an optimization criterion to assess the quality of the resulting communities. The Girvan–Newman algorithm for weighted graphs provides a powerful means of community detection, considering both the presence and strength of connections. This adaptation enhances its applicability to diverse systems where edge weights convey additional information about the underlying network structure.

Comparative Analyses

This study introduces five methodologies for comparing network communities. The initial approach involves comparing two distinct community detection methodologies implemented on the same network. The comparison includes the consideration of normalized mutual information, variation of information, split join distance, Rand index, and adjusted Rand index values.

When comparing two weighted network communities obtained by different community detection approaches, it is essential to employ appropriate evaluation metrics to assess the quality of identified communities. One commonly used metric is Normalized Mutual Information (NMI). NMI quantifies the mutual dependence between two sets of communities while considering variations in community sizes. The formula for NMI is given by

where \(I\left({{\mathcal{C}}}_{1};{{\mathcal{C}}}_{2}\right)\) represents the mutual information between the communities \({{\mathcal{C}}}_{1}\) and \({{\mathcal{C}}}_{2}\) , and \(H\left({{\mathcal{C}}}_{1}\right)\) and \(H\left({{\mathcal{C}}}_{2}\right)\) are the entropies of \({{\mathcal{C}}}_{1}\) and \({{\mathcal{C}}}_{2}\) , respectively. NMI ranges from 0 to 1, with higher values indicating greater similarity between community structures.

Variation of Information (VOI) is another crucial metric for community comparison. It captures both the uncertainty within individual communities and the uncertainty about the relationship between them. The formula for VOI is

where \(H\left({{\mathcal{C}}}_{1}\right)\) and \(H\left({{\mathcal{C}}}_{2}\right)\) are the entropies of \({{\mathcal{C}}}_{1}\) and \({{\mathcal{C}}}_{2}\) , respectively. Lower values of VOI correspond to better community detection results.

Split Join Distance (SJD) is a metric that measures the dissimilarity between two community structures by considering how communities split or merge. This metric is particularly suitable for detecting changes in community memberships. The formula for SJD is

where \(s\left({{\mathcal{C}}}_{1},{{\mathcal{C}}}_{2}\right)\) and \(s\left({{\mathcal{C}}}_{2},{{\mathcal{C}}}_{1}\right)\) represent the fraction of nodes split from \({{\mathcal{C}}}_{1}\) to \({{\mathcal{C}}}_{2}\) and from \({{\mathcal{C}}}_{2}\) to \({{\mathcal{C}}}_{1}\) .

Rand Index (RI) and Adjusted Rand Index (ARI) are widely used metrics for assessing the similarity between two sets of partitions. Rand Index quantifies the proportion of pairs of nodes that are correctly classified as either belonging or not belonging to the same community. The Adjusted Rand Index adjusts for chance agreement. The formulas for Rand Index and Adjusted Rand Index are

where \({c}_{1}\) is the number of pairs of nodes in the same community in both \({{\mathcal{C}}}_{1}\) and \({{\mathcal{C}}}_{2}\) , \({c}_{2}\) is the number of pairs of nodes in different communities in both \({{\mathcal{C}}}_{1}\) and \({{\mathcal{C}}}_{2}\) , and \({\mathbb{E}}\left[{RI}\left({{\mathcal{C}}}_{1},{{\mathcal{C}}}_{2}\right)\right]\) is the expected Rand Index.

This paper introduces a novel comparison methodology based on random walk that intends to evaluate networks obtained through various methods, in addition to the five existing methodologies for comparing network communities. In a random walk on a weighted network where lower edge weights signify stronger relationships, we can represent the process mathematically using equations that reflect this inverse relationship.

Let us consider a network represented by \(G=(V,{E}_{F},\omega )\) . Each edge \({e}_{{ij}}\in {E}_{F}\) connecting nodes i and j has an associated weight \({w}_{{ij}}\) . In this network, a lower weight implies a stronger relationship, so the transition probability from node i to node j is inversely proportional to the weight \({w}_{{ij}}\) . The transition probability \({P}_{{ij}}\) for a walker to move from node i to node j is given by:

where \(N(i)\) denotes the set of neighbours of node i , and \({w}_{{ik}}\) are the weights of the edges connecting node i to its neighbours. Here, \(1/{w}_{{ij}}\) represents the ‘strength’ of the connection, and the denominator is the normalization factor ensuring that the sum of probabilities from node i to all its neighbours equals 1.

Over time, the random walk can be analysed in terms of a Markov Chain, whose transition matrix M is defined by the probabilities \({P}_{{ij}}\) . The state of the walker after n steps is given by the distribution vector \({{\boldsymbol{v}}}^{\left(n\right)}\) , where

and \({{\boldsymbol{v}}}^{\left(0\right)}\) is the initial state of the walker.

In the long run, the system may reach a steady state described by a stationary distribution Π , where \({\boldsymbol{\Pi }}{\boldsymbol{M}}={\boldsymbol{\Pi }}\) . This stationary distribution depends intricately on the network’s topology and the inverse weighting of the edges, providing insights into the most ‘strongly connected’ components of the network. This mathematical framework is valuable for understanding various real-world networks, such as financial networks, where stronger ties have less ‘resistance’ or ‘distance’ and thus are more frequently traversed in the random walk process.

Over a sufficiently extended period, the random walker can visit every node in the network. By defining the transitions of the random walker, some nodes will be visited with varying frequencies. Therefore, over time, each node can be assigned distinct values based on their centrality within the network. Given that all networks in this study have the same set of nodes, we begin the random walker at the first node, which is labelled as 1 in the node list. We then proceed with the random walk procedure. The visited nodes will generate a series of values. The methodology employed in this study relies on the calculation of transfer entropy between the series under investigation. When computing the transfer entropy, we examine a process similar to the one outlined in Eq. 8 .

The Borsa Istanbul Sustainability Index (XUSRD) is an important initiative by Borsa Istanbul aimed at promoting and highlighting sustainable business practices among the companies listed on the exchange.

The XUSRD Index, introduced on November 4, 2014, aims to assist organizations in formulating policies that consider the potential risks associated with ESG (Environment, Social, Governance) matters. Additionally, it seeks to educate investors about the sustainability practices implemented by these companies. To qualify for inclusion in this index, organizations must meet certain requirements, including a cumulative ESG score of 50 or higher, individual scores of 40 or higher for each of the ESG pillars, and at least 8 category scores of 26 or higher. As of 2023, the Borsa Istanbul Sustainability Index includes 80 companies.

This index provides a competitive edge to Turkish organizations that effectively manage their corporate risks and opportunities. It serves as a benchmark for organizations to assess and improve their sustainability performance, thereby increasing their visibility, reputation, and potential to attract global investments and clients. The index is based on evaluations conducted by Refinitiv Information Limited using publicly available data, and costs associated with assessing companies are funded by Borsa Istanbul (Hizarci-Payne & Kirkulak-Uludag, 2018 , Yılmaz et al., 2020 ).

Borsa Istanbul’s adoption of this index reflects its commitment to sustainability and responsible investment, aligning with the growing global focus on environmental, social, and governance matters. The index incentivizes organizations to continually enhance their sustainability performance, serving as a measurable standard for the creation of various financial instruments such as funds, exchange-traded funds, and structured products that adhere to sustainability principles.

We omitted KRDMR due to its missing values within the specified time frame. Furthermore, we omitted ISBTR because the ISCTR code is also a representation of the same corporation. The time series data used in this study originated from the 78 companies traded in XUSRD. Each time series has 249 observations and includes the daily closing prices of companies traded in each index. Descriptive statistics for the dataset are provided in Table A1 .

Choosing the Borsa Istanbul Sustainability Index for network analysis, with an emphasis on sustainability and corporate responsibility, offers several advantages compared to the broader Borsa Istanbul 100 Index. The Borsa Istanbul Sustainability Index is a specialized index comprising companies that demonstrate exceptional sustainability performance. This focus allows for a detailed examination of how sustainability impacts company networks, investor relations, and market behaviours, highlighting the increasing significance of sustainability in investment decisions. Additionally, by evaluating the included companies based on these criteria, the index provides a unique perspective on ESG concerns. This enables an understanding of the interaction between ESG variables and company policies, which is less apparent in more comprehensive indices such as the Borsa Istanbul 100 Index. Examining the Borsa Istanbul Sustainability Index can uncover novel and insightful market patterns due to the dynamic nature of sustainability in stock indices. Moreover, companies that prioritize sustainability often exhibit greater resilience to environmental and social risks, providing valuable insights into risk management strategies that enhance corporate stability.

ESG scores are specifically formulated to assess a company’s proficiency in addressing diverse sustainability and ethical obstacles. The ratings are divided into various essential sections, each emphasizing different aspects of a company’s operations and influence.

The emissions score assesses a company’s greenhouse gas emissions, considering both the overall emissions generated and the intensity of those emissions in relation to company production. It discusses the company’s efforts to control and diminish these emissions through diverse programs and adherence to environmental rules. The resource use score evaluates the effectiveness and long-term viability of a company’s utilization of natural resources. Important indicators include quantifying water and energy consumption, the amount of trash produced and recycled, and the utilization of sustainable resources. In this area, companies that successfully execute efficient resource management techniques achieve better scores. The innovation score evaluates a company’s allocation of resources towards research and development (R&D) and its capacity to generate novel ideas and solutions that promote sustainability. This includes the creation of novel technologies and goods that minimize harm to the environment, as well as the acquisition of patents pertaining to sustainable technologies. The human rights score focuses on analysing a company’s policies and practices related to safeguarding human rights in its operations and supply chain. It covers topics such as workers’ rights, equitable remuneration, discrimination regulations, and initiatives to combat child and coerced labour. The product responsibility score assesses a company’s ability to effectively handle the safety, quality, and environmental consequences of its products. It encompasses factors such as adherence to product safety regulations, assessment of the environmental impact throughout the product lifecycle, and the incorporation of sustainable materials in the product development process.

The workforce score evaluates how a company treats its employees, with a specific focus on labour practices, employee health and safety, training and development opportunities, and activities related to diversity and inclusion. Companies that cultivate a constructive and fair work atmosphere typically achieve higher scores. The community score is used to measure a company’s level of involvement and influence in the communities where it operates. It includes humanitarian endeavours, community development initiatives, and efforts to address local concerns and make a positive impact on society. The management score domain assesses the calibre and efficiency of a company’s governance structures and processes. This includes the board structure and diversity, executive remuneration, risk management, and overall corporate governance regulations. The shareholder score evaluates how a company prioritizes and resolves its shareholders’ interests and concerns. It considers factors such as transparency, communication, and the company responsiveness to shareholder resolutions and suggestions. The corporate social responsibility (CSR) strategy score evaluates a company’s comprehensive approach to integrating social and environmental factors into its commercial strategy. The CSR framework encompasses company’s dedication to CSR values, execution of CSR initiatives, and documentation of CSR actions and results.

Table A2 details the ESG and sub-scores for each company analysed in this study. These scores are based on self-reported data from each company for the fiscal years 2022 or 2023. The ESG scores encompass a range of subcategories, including Emissions, Resource Use, Innovation, Human Rights, Product Responsibility, Workforce, Community, Management, Shareholders, and CSR Strategy. Each sub-score provides insight into specific aspects of a company’s environmental, social, and governance practices, offering a comprehensive view of their sustainability performance.

The goodness-of-fit metrics provided in Table 1 shed light on the effectiveness of the linear regression model in explaining the variability in ESG scores of companies in the Borsa Istanbul Sustainability Index. Adjusted R -squared value of 0.9402 suggests that the model can account for approximately 94% of the variability in ESG scores, considering the number of predictors. The adjusted R -squared is particularly useful because it adjusts for the number of variables in the model, preventing overestimation of the model’s explanatory power. A value close to 1 suggests a very good fit. The Akaike Information Criterion (AIC) is a measure of the relative quality of statistical models for a given dataset. It provides a means for model selection, with lower values indicating a better-fitting model. In this context, an AIC of 377.12 suggests that the model is relatively efficient in balancing goodness-of-fit and complexity. The Bayesian Information Criterion (BIC) is another criterion for model selection, similar to AIC, but with a stricter penalty for models with more parameters. A lower BIC indicates a better model fit. The BIC value of 405.44 suggests that, while the model is complex, it balances this complexity with data fit. The R -squared value of 0.948 indicates that the model explains about 94.8% of the variability in ESG scores. It is a measure of how well the regression predictions approximate the real data points. A value close to 1 indicates the strong explanatory power of the model. In summary, the high R -squared and adjusted R -squared values indicate that the model is highly effective in explaining the variability in ESG scores. Although AIC and BIC values suggest some model complexity, they support the model fit and efficiency.

The linear regression model in Table 2 provides useful insights into the impact of many factors on the ESG ratings of companies in the Borsa Istanbul Sustainability Index. The intercept, with an estimated value of 4.911, is not statistically significant. This means that the basic ESG score, when all other factors are held constant, does not provide meaningful information on its own. The coefficient for Emission is positive (0.0279) but lacks statistical significance, suggesting that emission levels have a negligible and non-significant influence on ESG ratings. On the other hand, there is a strong and positive link between Resource Use and ESG ratings, as indicated by a coefficient of 0.117 and a p -value of \(6.7\times {10}^{-6}\) . This implies that effective allocation of resources is closely linked to improved ESG performance.

The impact of Innovation on ESG scores is extremely significant, as evidenced by a coefficient of 0.054 and a p -value of \(6.6\times {10}^{-6}\) . This shows the crucial role of innovation in attaining higher ESG ratings. The analysis indicates that there is a substantial and positive relationship between human rights practices and ESG scores. The coefficient of 0.05 and the p -value of 0.039 provide statistical evidence for this relationship. It suggests that organizations with stronger human rights practices generally get higher ESG scores. The coefficient of 0.089 and the p -value of 0.00014 indicate that there is a strong link between product accountability and higher ESG ratings. This means that organizations that accept responsibility for their goods are more likely to have better ESG scores. Workforce, with a coefficient of 0.173 and a p -value of \(6.7\times {10}^{-6}\) , exhibits a statistically significant positive relationship with ESG scores. Hence, implementing effective workforce practices is crucial for attaining high ESG ratings. The statistical analysis reveals that community participation has a coefficient of 0.14 and a p -value of \(1.5\times {10}^{-8}\) , indicating a high level of significance. This emphasizes the crucial role of community involvement in improving ESG performance. The analysis reveals a significant and positive relationship between management practices and ESG scores. The coefficient of 0.197 indicates a substantial impact, while the p -value of \(1.3\times {10}^{-21}\) suggests a highly significant relationship. These findings underscore the importance of Management in achieving high ESG scores. The impact of Shareholders on ESG ratings is substantial, as indicated by a coefficient of 0.041 and a p -value of 0.00117. This suggests that active shareholder participation has a favourable effect on ESG scores. Furthermore, the coefficient of CSR Strategy is 0.036 with a p -value of 0.0188, suggesting that a strong CSR strategy is linked to elevated ESG scores.

ANOVA results in Table 3 provide an in-depth analysis of the impact of various factors on the ESG scores of companies included in the index. Each factor is evaluated in terms of its contribution to the overall model and its statistical significance, as indicated by the sum of squares (SS), mean squares (MS), F -statistics, and p -values.

Emission shows an F -statistic of 224.437 with a highly significant p -value of \(4.5\times {10}^{-23}\) , indicating a substantial impact on ESG scores. Resource Use has an F- statistic of 418.749 and a p -value of \(1.5\times {10}^{-30}\) , highlighting its critical importance in the model. Innovation, with an F -statistic of 27.1374 and a p -value of \(1.9\times {10}^{-6}\) , also significantly influences ESG scores. Human Rights is another highly significant factor, reflected by its F -statistic of 123.313 and a p -value of \(7.7\times {10}^{-17}\) . Product Responsibility shows a moderate significance with an F -statistic of 4.46292 and a p -value of 0.038. Workforce management is strongly significant, indicated by an F -statistic of 152.156 and a p -value of \(6.6\times {10}^{-19}\) . Community involvement also plays a significant role, with an F -statistic of 58.7096 and a p -value of \(9.9\times {10}^{-11}\) . Management practices, with an F -statistic of 194.79 and a p -value of \(1.6\times {10}^{-21}\) , underscore the importance of governance. Shareholders’ involvement is significant, as shown by an F -statistic of 11.0519 and a p -value of 0.00144. Finally, the CSR Strategy demonstrates significance with an F -statistic of 5.79067 and a p -value of 0.01887. These results collectively confirm that factors significantly impact ESG scores, reflecting their multifaceted roles in sustainability performance.

Our study uses the ESG scores of companies in the XUSRD dataset, which is highly suitable for examining the impact of various factors on community formation in different network types (correlation networks, mutual information networks, causality networks). The relevance of ESG scores lies in their comprehensive measure of a company’s performance across environmental, social, and governance dimensions, which aligns perfectly with our aim to investigate the factors influencing community formation based on ESG-related criteria. The dataset includes a diverse range of variables, ensuring a comprehensive analysis of these factors. The high adjusted R -squared value demonstrates statistical robustness, indicating that the model explains a substantial portion of the variance in ESG scores. This provides confidence in the ability of data to reveal meaningful patterns and relationships. With data from 78 companies and 249 observations for each time series, the dataset is sufficiently large to allow for robust statistical analyses, making the findings generalizable and not biased by the small sample size.

The subsequent part of this section encompasses networks acquired using various techniques, as well as the graph communities derived from these networks. Such networks are constructed based on distinct methodologies including correlation distance, mutual information (both continuous and discrete), and causality (linear and nonlinear). Each method provides a unique perspective on the interactions and dependencies among companies in the Borsa Istanbul Sustainability Index, highlighting different aspects of their relationships.

The figures used in the following subsections incorporate colour-coded indications to represent sectors to which companies belong, facilitating a visual understanding of sector-specific clustering and community formation. The node colours represent the sectors of each company according to the following rule: red represents commercial, green represents energy, blue represents finance, yellow represents manufacturing, orange represents technology, black represents transportation. This colour-coding scheme allows for an intuitive comparison of sectoral distribution within and across the different network types.

Results on correlation networks

The correlation network depicted on the left side of Fig. 1 illustrates the interconnectedness of companies based on the correlation of their daily closing prices, with nodes colour-coded by sector. The network topology reveals clusters of companies, signifying strong intra-sector connections, especially among manufacturing companies that typically display higher vertex degrees. This suggests that companies within the same sector tend to have more similar stock price movements, reflecting shared market influences and sector-specific factors. The weighted vertex degree distribution on the top right shows that most companies have a moderate number of connections, with some having significantly higher connectivity, reflecting their central role in the network. The edge weight distribution on the bottom right indicates that most connections between companies are relatively strong, as evidenced by the clustering of edge weights around higher values. This suggests robust correlations in daily closing prices between many companies, highlighting the significant influence of market dynamics and sector-specific trends within the network. Overall, the network topology and distributions suggest a well-connected structure, with certain sectors, particularly manufacturing, playing a pivotal role in market dynamics.

TMFG with correlation distance and weighted degree distribution.

Figure 2 shows the clustering results of the correlation network based on company daily closing prices, with clusters identified using the Leading Eigenvector method on the left and the Girvan–Newman method on the right.

Emerging filtered correlation network communities.

In Fig. 2 both methods reveal distinct communities within the network, with nodes colour-coded by sector, as mentioned before. The Leading Eigenvector method identifies several well-defined clusters, indicating strong intra-sector correlations, particularly within the manufacturing and financial sectors, which appear to form tight-knit groups. This suggests that companies within these sectors exhibit similar stock price movements, likely driven by sector-specific factors and market conditions. Similarly, the Girvan–Newman method also identifies distinct communities, though the clustering patterns show slight variations compared to the Leading Eigenvector method. The financial and manufacturing sectors again show significant clustering, highlighting their strong internal correlations. Both methods reveal that companies within the same sector tend to cluster together, reflecting shared market influences and sectoral trends. Overall, clustering results from both methods show how important sectoral affiliation is in determining how daily closing prices are correlated, with clear community structures showing up in the manufacturing and financial sectors. It indicates that these sectors have more homogenous price movements, likely due to common economic drivers and market conditions.

Table A3 shows the community results that indicate how the Leading Eigenvector and Girvan–Newman algorithms found communities in the correlation network. Each community includes companies from diverse sectors. This diversity within communities indicates that companies from distinct sectors exhibit significant correlations in daily closing prices, likely reflecting interconnected market behaviours and shared external influences. For instance, in Community 1, one sees a mix of financial, manufacturing, and energy companies, suggesting that sectors may be highly correlated in their stock price movements. The presence of companies from multiple sectors within each community is consistent with previous research on significant sectoral interdependencies in the Borsa Istanbul market. Moreover, the weighted vertex degree and eigenvector centrality metrics emphasize the roles and significance of specific companies within their respective communities. In Community 1, for example, companies in the commercial sector like MGROS have a high-weighted vertex degree of 3.67612 and an eigenvector centrality of 0.0601084, which shows that they have a lot of strong connections and influence in the network. Similarly, in the financial sector, ISGYO has a weighted vertex degree of 4.43027 and an eigenvector centrality of 0.0735354, highlighting its critical role in the network structure. In Community 3, TOASO from the manufacturing sector has a weighted vertex degree of 3.41767 and an eigenvector centrality of 0.2251145, making it a central player in maintaining network cohesion.

Results on mutual information networks

This study employs the Kraskov estimator (Kraskov et al., 2004 ) to compute the continuous mutual information values for logarithmic returns of daily closing prices of the companies listed in the XUSRD index.

Figure 3 highlights a network derived from continuous mutual information between company daily closing prices, displayed on the left side.

TMFG with continuous mutual information and weighted degree distribution.

The network topology reveals a high degree of interconnectedness, particularly among the financial and manufacturing sectors, which exhibit higher vertex degrees in Fig. 3 . This indicates that sectors share significant informational dependencies, reflecting similar responses to market conditions. The weighted vertex degree distribution, shown on the top right, highlights that most companies have a moderate number of connections, with a few companies having very high degrees, indicating their central role in the network. The centrality of these companies implies their status as key players, closely monitored and highly influential in stock price movements. The edge weights distribution, depicted on the bottom right, shows that most connections have relatively high weights, indicating strong mutual information between closing prices of companies. This suggests that company stock prices contain significant shared information, likely driven by sector-specific dynamics and overall market trends. Network topology and distributions indicate a robust structure, with certain sectors, particularly financials, and manufacturing, playing pivotal roles in the mutual information network based on daily closing prices. This reflects substantial informational linkages within these sectors, emphasizing their importance in the market’s overall behaviour.

Figure 4 displays communities identified in the continuous mutual information network based on company daily closing prices.

Emerging filtered continuous mutual information network communities.

In Fig. 4 , the left side, derived by using the Leading Eigenvector method, reveals four distinct communities. Community 1 and Community 4 predominantly consist of companies from the financial and manufacturing sectors, with strong intra-sector information sharing. Community 2 and Community 3 include a mix of sectors, highlighting inter-sector dependencies. On the right, the Girvan–Newman method also identifies four communities, but with different compositions. While Community 2 centres around a few key financial and commercial companies, Community 1 is diverse, containing companies from various sectors. Community 3 and Community 4 display a blend of manufacturing and technology sectors, illustrating sectoral and cross-sectoral informational relationships. Both methods highlight that companies within the same sector tend to cluster together due to strong mutual information links, reflecting similar market behaviours and shared influences. The variations in community structure between methods underscore different perspectives on how these informational relationships manifest within the network. Overall, clustering results emphasize the significant role of sectoral affiliations in shaping the network topology based on daily closing prices, with the financial and manufacturing sectors showing particularly strong internal and external connections.

In Table A4 , presenting continuous mutual information network communities, we observe the significance of weighted vertex degree and eigenvector centrality metrics in identifying pivotal companies within their respective communities. For example, in the Leading Eigenvector community, the company DOAS in the commercial sector exhibits a high-weighted vertex degree of 13.4232 and an eigenvector centrality of 0.0527802, indicating its central role in network connectivity. Similarly, in the Girvan–Newman community, the company MAVI, also in the commercial sector, displays a notable weighted vertex degree of 51.0328 and an eigenvector centrality of 0.0634826, highlighting its influence within the network structure. These metrics underline the importance of certain companies in maintaining the overall network integrity and their potential impact on market dynamics. By examining these values, one can infer that companies with higher degrees and centrality are likely to be influential in driving the behaviour and performance of their communities, thereby playing crucial roles in market sustainability and stability. For instance, companies like AGESA in the financial sector and KORDS in the manufacturing sector also show significant metrics, reinforcing their key positions in the network.

Figure 5 presents the network based on discrete bivariate mutual information between company daily closing prices.

TMFG with discrete bivariate mutual information and weighted degree distribution.

The network topology shows that the manufacturing and financial sectors are closely connected in Fig. 5 , which means that they share a lot of information. This is probably because of factors that are specific to each sector and the way markets are set up. The weighted vertex degree distribution on the top right shows that most companies have a moderate number of connections, with a few companies exhibiting high connectivity, suggesting their central role in the network. Central companies are likely influential in the market, as their price movements provide significant informational content for other companies. The edge weight distribution on the bottom right shows that most connections have high mutual information values, indicating strong relationships between company closing prices. The high mutual information suggests that stock price movements share substantial information, potentially due to shared economic influences or sector-specific dynamics. Overall, the network topology and distributions show that sectors like manufacturing and finance are very important, with a lot of information flowing within and between sectors. This underscores the importance of these sectors in the overall market behaviour, as reflected by the discrete bivariate mutual information derived from daily closing prices.

Figure 6 displays communities identified using discrete bivariate mutual information between daily closing prices, with results from the Leading Eigenvector method on the left and the Girvan–Newman method on the right.

Emerging discrete bivariate mutual information network communities.

The Leading Eigenvector method reveals two major communities in Fig. 6 . Community 1 consists primarily of a mix of financial and manufacturing companies, indicating strong intra-sector mutual information linkages. Community 2 also includes a diverse mix of sectors, highlighting the presence of inter-sector dependencies and shared market behaviours. The Girvan–Newman method identifies four distinct communities. Community 1 is diverse, comprising companies from various sectors, which suggests significant cross-sectoral informational relationships. Community 2 and Community 4 display clusters of manufacturing and financial companies, respectively, reflecting strong sector-specific mutual information linkages. The transportation and energy sectors notably centre in Community 3, indicating specialized inter-sectoral connections. The methods indicate that companies within the same sector tend to form clusters due to high mutual information values, reflecting similar stock price movements driven by common economic factors and sector-specific trends. The differences in community structures between the two methods provide complementary views on how informational relationships manifest within the network, emphasizing both intra-sector and cross-sector dependencies in the financial market. Overall, these clustering results highlight the crucial role of sectoral affiliation in forming a mutual information network based on daily closing prices, particularly emphasizing the financial and manufacturing sectors.

In the discrete bivariate mutual information network, community structures reveal different dynamics, as can be seen in Table A5 . For example, companies like BIMAS in the commercial sector and TUPRS in manufacturing stand out with high-weighted vertex degrees and significant eigenvector centrality. BIMAS, with a weighted vertex degree of 12.8068 and an eigenvector centrality of 0.0327421, is a key player within its community, indicating strong interconnections and influence. This centrality suggests that BIMAS is crucial for the robustness and cohesion of its network cluster. In the manufacturing sector, TUPRS shows a significant presence with a vertex degree of 8.4654, reflecting its substantial role in community connectivity and information dissemination.

Results on causality networks

Figure 7 displays the network, its weighted vertex degree distribution, and edge weights, as well as the network that has been thresholded using the p -values of the linear casualty test. For the linear causality test, we use the order of 1.

TMFG with linear causality and weighted degree distribution.

The network topology in Fig. 7 shows a well-connected structure with several clusters, particularly within the financial and manufacturing sectors, indicating strong linear causal relationships among companies. This suggests that stock price movements in these sectors can predict each other, reflecting shared market influences and sector-specific dynamics. The weighted vertex degree distribution on the top right reveals that most companies have a moderate number of connections, with a few having very high connectivity, indicating their significant influence within the network. These central companies are likely key players whose price movements are pivotal in driving overall market trends. The edge weight distribution on the bottom right shows that most connections have high weights, indicating strong linear causality between company closing prices. This suggests that the price movements of these companies are highly predictive of each other, further emphasizing the interdependence within sectors. Overall, the network topology and distributions suggest a robust structure, with certain sectors, particularly financial and manufacturing, playing pivotal roles. The presence of strong linear causal relationships highlights the importance of these sectors in the market’s overall behaviour, as reflected by daily closing prices.

Using the Leading Eigenvector and the Girvan–Newman algorithm, the network communities depicted in Fig. 8 were generated.

Emerging filtered linear causality network communities.

Figure 8 shows the communities identified in the linear causality network based on company daily closing prices, using the Leading Eigenvector method on the left and the Girvan–Newman method on the right. The Leading Eigenvector method reveals six communities. Financial and manufacturing companies primarily compose Community 1 and Community 2, indicating strong intra-sector linear causal relationships. Communities 3–5 include a mix of sectors, suggesting the presence of significant inter-sector dependencies. Community 6 shows a smaller cluster with notable interactions within the energy sector. The Girvan–Newman method identifies seven communities with a slightly different structure. While Community 3 and Community 4 centre around key financial and commercial companies, reflecting strong internal causal influences, Community 1 and Community 2 also display a mix of sectors. Communities 5–7 demonstrate clusters that include companies from various sectors, underscoring inter-sectoral causal connections. Both methods highlight that companies within the same sector tend to form clusters due to strong linear causal relationships, indicating that their stock price movements are predictive of each other.

Table A6 displays linear causality network communities. It shows that financial companies such as AKBNK and GARAN are at the centre of Community 1, which means they play a big part in how the network changes over time based on linear causal relationships derived from daily closing prices. Similarly, Community 2 also features key financial players such as HALKB and ISCTR, highlighting the strong interconnections within the financial sector. Conversely, Communities 3 and 4 prominently group manufacturing companies such as TOASO, VESTL, and ARCLK. This pattern shows that linear causality is a good way to explain sector-based clustering. It shows how network causal influences line up with the boundaries between sectors. Interestingly, the Leading Eigenvector and Girvan–Newman community detection methods consistently observe these sectoral clusters, demonstrating their robustness in identifying meaningful community structures. Moreover, the weighted vertex degree and eigenvector centrality metrics further emphasize the importance and connectivity of these companies within their respective communities, highlighting their pivotal roles in market dynamics. For example, AKBNK and GARAN exhibit high vertex degrees and eigenvector centrality, indicating their influential positions within the financial sector. Similarly, manufacturing giants like TOASO and VESTL show significant centrality metrics within their clusters, underscoring their critical roles in the manufacturing sector’s network dynamics.

Figure 9 displays the thresholded network, along with its weighted vertex degree and edge weight distributions, as well as the p -value of nonlinear casualty. The following parameters are set for the computation of nonlinear casualty: with a learning rate of 0.01 and a number of iterations set to 50, the hidden layer size for the bivariate model is 4 and that for the univariate model is 2. Additionally, the stochastic gradient descent algorithm is employed.

TMFG with nonlinear causality and weighted degree distribution.

The network topology depicted in Fig. 9 exhibits a complex and interdependent structure with multiple core nodes, particularly within the banking and manufacturing sectors. This suggests the presence of robust nonlinear causal linkages among these organizations. The upper right corner displays the vertex degree distribution, which accounts for the weights of the connections. It indicates that most companies have a moderate number of connections, while certain organizations have a significantly high degree, suggesting their central position in the network. These pivotal companies are important actors whose unpredictable price swings have a substantial impact on other enterprises in the network. The distribution of edge weights, shown in the bottom right, reveals that most connections have high weights, showing a significant nonlinear causation between company closing prices. The closely connected price fluctuations of these companies highlight intricate connections among sectors. In general, the network topology and distributions indicate a strong and resilient structure, with the financial and manufacturing sectors playing important roles.

Figure 10 shows the nonlinear network communities that were detected by using the Leading Eigenvector and the Girvan–Newman algorithm.

Emerging filtered nonlinear causality network communities.

In Fig. 10 , the Leading Eigenvector method reveals six communities. Manufacturing and financial companies predominantly compose Community 1 and Community 4, indicating strong intra-sector nonlinear causal relationships. Communities 2, 3, and 5 include a diverse mix of sectors, highlighting significant inter-sector dependencies. Community 6 shows a cluster primarily centred around the commercial sector, with sector-specific nonlinear interactions. The Girvan–Newman method identifies nine communities, with Community 4 being the largest and most central, incorporating a mix of sectors that suggests significant cross-sectoral nonlinear causal relationships. Community 1 and Community 2 display a concentration of financial and manufacturing companies, indicating strong sector-specific nonlinear influences. Communities 5 through 9 demonstrate smaller clusters, often involving a combination of sectors, underscoring the presence of inter-sectoral interactions. Both methods stress that companies in the same sector tend to group together because of strong nonlinear causal relationships. This is because similar stock price changes are caused by complex market dynamics and factors that are unique to the sector. Mixed-sector communities are present in both methods, indicating significant cross-sectoral interactions within the market.

Table A7 illustrates the nonlinear causality network communities, showcasing a diverse clustering pattern based on nonlinear relationships between company daily closing prices. Community 1 prominently features energy companies like ZOREN and manufacturing companies like SISE and TOASO, indicating strong nonlinear causal connections within these sectors. Financial firms like GARAN and manufacturing companies like EREGL are central in Community 2, highlighting their significant roles in nonlinear interactions. This table confirms that nonlinear causality induces a unique clustering dynamic that intertwines multiple sectors, differing from linear causality, which predominantly segregates sectors. The presence of companies from different sectors within the same community emphasizes the complex, multifaceted nature of nonlinear relationships in financial markets. This intricacy is evident in companies such as AKBNK and TUPRS, which exhibit high eigenvector centrality and influence, playing pivotal roles across multiple communities. This further underscores the importance of considering nonlinear causality to fully understand the interdependencies and the structural topology of financial networks.

Results of network and community comparisons

Figure 11 displays the series that were derived from the edge evaluation using a random walker with a larger transition probability compared to low edge weights. A random walk method with 10,000 steps was chosen.

Node visiting values of random walker for different networks.

In Fig. 11 , in the correlation network, specific vertices exhibit very high visit frequencies, indicating their significant centrality and influence within the network. Similar patterns emerge in the continuous and discrete mutual information networks, where certain nodes receive more frequent visits, indicating their crucial roles in information sharing. Linear causality network reveals prominent nodes with high visit frequencies, emphasizing their strong predictive relationships. Nonlinear causality network displays a more distributed pattern, with several vertices showing high centrality, reflecting complex nonlinear dependencies.

To determine the transfer entropy, we adhere to the steps described by Behrendt et al. ( 2019 ). By setting the lags for series to 1, we enable the function to consider the impact of previous values on subsequent ones. We usually set the quantile threshold for calculating transfer entropy at 0.1 to give more weight to extremes of distributions. We use Shannon’s entropy to calculate the transfer entropy. We sort data into quantiles, bins, and limits, then shuffle the data 100 times. We determine the uncertainty of the transfer entropy estimate using 300 bootstrap samples and maintain the stability of the bootstrap estimate by discarding 30 initial samples.

The resulting transfer entropies in the form of \({G}_{F}1\to {G}_{F}2\) are presented in Table 4 .

The values in Table 4 show transfer entropies between various types of networks, including correlation, continuous mutual information, discrete mutual information, linear causality, nonlinear causality. These values come from random walker distribution. Transfer entropy quantifies the amount of directed (asymmetric) information transferred between two processes, in this case, different network structures. Higher values indicate greater predictability or influence from one network to another. Starting with the correlation network, we see relatively high transfer entropy values when compared to other networks, with the highest influence observed towards the nonlinear causality network (0.028385). This suggests that information flows from the correlation network to the nonlinear causality network is significant, indicating that relationships captured by the correlation are relevant to the nonlinear dependencies.

The linear causality network has the highest transfer entropy for the continuous mutual information network (0.0333629). This means that continuous mutual information is most useful for understanding linear causal relationships. This highlights the importance of mutual information in understanding linear dependencies in the network. The discrete mutual information network has moderate transfer entropy values across all other networks, with the highest influence on the linear causality network (0.0280271). Discrete mutual information captures substantial interactions, which linear causality also reflects. The nonlinear causality network receives the highest transfer entropy (0.039678) from the linear causality network, indicating a strong influence of linear causal relationships on nonlinear dependencies. This high value suggests that linear causality encapsulates critical aspects of the dynamics that are further detailed in nonlinear interactions.

Finally, the nonlinear causality network shows significant transfer entropy towards the linear causality network (0.113118), the highest observed in the table. This shows how complicated and two-way this influence is between linear and nonlinear causal networks. It also shows how nonlinear dependencies offer a bigger picture to understand linear causal effects. In summary, transfer entropy values illustrate the interconnectedness and predictive power between different network types. Both linear and nonlinear correlation and causality networks have significant values. This suggests that these networks are capturing important, overlapping parts of financial data.

In addition to looking at the topological structures of networks that were made, it is also important to look at how well communities that were created using two different approaches can cluster. Table 5 displays the outcomes for comparative metrics specified in the preceding sections.

Community comparison metrics in Table 5 provide a comprehensive evaluation of community detection performance across different network types. The correlation network shows a moderate VOI of 1.126, indicating a relatively average level of information loss between true and detected communities. Its NMI of 0.588348 suggests a decent alignment of detected communities with true communities. The SJD of 42, RI of 0.8022, and ARI of 0.4722 further confirm that while communities are reasonably accurate, there is room for improvement in capturing the intricate structures within the network. The continuous mutual information network has the highest VOI of 1.715, indicating significant information loss and less effective community detection. Its NMI is the lowest at 0.3039, reflecting poor correspondence with true communities. The high SJD of 66 also points to considerable discrepancies in community structure, while the RI (0.6567) and ARI (0.1977) indicate relatively weak community detection performance. In contrast, the discrete bivariate mutual information network performs better with a lower VOI of 1.102 and a moderate NMI of 0.4528. The SJD of 37 suggests a more accurate community structure compared to the continuous counterpart. The RI of 0.7126 and ARI of 0.422 indicate an overall moderate performance, balancing between information preservation and accurate community detection. The linear causality network exhibits the best performance, with the lowest VOI of 0.866, indicating minimal information loss. Its NMI of 0.7593 is the highest among all networks, showing strong alignment with true communities. The SJD of 32, along with high RI (0.899) and ARI (0.6356), demonstrates superior community detection accuracy, capturing directed influences effectively.

Finally, the nonlinear causality network has the lowest VOI of 0.573, indicating the least information loss. Its NMI of 0.573 suggests good correspondence with true communities, although not as high as the linear causality network. The SJD of 53 indicates some discrepancies in community structure, but the RI (0.8151) and ARI (0.3471) reflect a strong performance, particularly in capturing nonlinear relationships.

Overall, these results highlight that while continuous mutual information struggles to capture community structures effectively, linear and nonlinear causality networks provide more accurate and robust community detection, reflecting their capability to model complex dependencies in financial networks. The correlation network offers balanced performance, but improvements can be made by leveraging causality-based methods to capture deeper insights into community structures.

Discussions

The next phase of this study involves examining how Environmental, Social, and Governance (ESG) scores impact the clustering of companies within these networks. By performing nonparametric tests on the ESG scores, we aim to determine whether these sustainability metrics significantly affect the formation and structure of communities within the various network models. This analysis will provide insights into the role of ESG factors in shaping financial networks and their potential to drive sustainable investment practices.

We will use nonparametric tests like the Kruskal–Wallis, Conover, and Gehan to evaluate how ESG scores impact clustering patterns in networks. These tests are particularly suitable because they do not assume a specific data distribution, making them robust for evaluating the relationships between ESG scores and community formation. By utilizing these tests, we can rigorously evaluate whether differences in ESG scores across various clusters are statistically significant, providing a deeper understanding of how sustainability practices influence network topology.

In this context, we will analyse several ESG sub-scores, including Emission, Resource Use, Innovation, Human Rights, Product Responsibility, Workforce, Community, Management, Shareholders, and CSR Strategy. Each of these sub-scores represents a critical aspect of a company sustainability performance and can provide nuanced insights into how different elements of ESG influence network dynamics. For instance, higher scores in Innovation or Resource Use might be indicative of companies that are more central in certain network communities due to their advanced practices and efficient operations.

We will treat ESG scores as an independent variable and the community memberships obtained from the various network models as dependent variables. By comparing the distribution of ESG scores across different communities, we can identify whether certain sustainability practices are more prevalent in specific clusters, indicating a correlation between ESG performance and network position. This approach will help in understanding whether companies with superior ESG metrics tend to cluster together, potentially due to similar strategic goals or operational practices that align with sustainability principles.

Furthermore, this analysis will explore whether certain ESG dimensions are more influential in determining community structure within specific types of networks. For example, in correlation networks, we might find that companies with high Human Rights scores cluster together, reflecting their commitment to social governance aspects. In contrast, in mutual information networks, Innovation scores might play a more significant role in community formation, highlighting the importance of technological advancements and innovative practices in these clusters.

Table 6 presents the results of nonparametric tests for ESG scores across correlation network communities, highlighting significant findings for various sustainability metrics.

In Table 6 , the Kruskal–Wallis test results for the Leading Eigenvector method indicate that Product Responsibility ( \(p=0.061\) ) and Human Rights ( \(p=0.092\) ) are marginally significant, suggesting that these factors might influence community formation to some extent. The Conover test, however, shows a more pronounced significance for Resource Use ( \(p=0.017\) ), indicating a strong impact of resource management practices on community clustering. This is further supported by the log-rank test, which highlights Product Responsibility ( \(p=0.0425\) ) and Human Rights ( \(p=0.092\) ) as notable influencing variables.

For the Girvan–Newman method, the Kruskal–Wallis test reveals significant results for Innovation ( \(p=0.0265\) ) and CSR Strategy ( \(p=0.008\) ), suggesting these elements are key drivers in community formation. The Conover test corroborates the significance of Resource Use ( \(p=0.0182\) ) and Innovation ( \(p=0.0748\) ), indicating consistent findings across different test methodologies. The log-rank test underscores the importance of CSR Strategy ( \(p=0.005\) ) and Innovation ( \(p=0.012\) ), further validating the influence of ESG factors on network communities.

When the findings from the correlation network topologies are considered alongside the results of the nonparametric tests for ESG scores, a nuanced picture emerges. The nonparametric tests, particularly the Conover test for the Leading Eigenvector method, indicate that Resource Use significantly affects community formation. This suggests that companies with similar resource use practices are more likely to cluster together within the network, reinforcing the idea that sustainability strategies are a critical factor in driving stock price correlations. The log-rank test further supports this by highlighting the significance of Product Responsibility ( \(p=0.0425\) ) and Human Rights, indicating that these ESG factors also influence clustering.

For the Girvan–Newman method, the nonparametric tests underscore the importance of Innovation and CSR Strategy, suggesting that companies with strong innovation and CSR strategies tend to form distinct communities. This aligns with the observed clustering patterns, where companies with similar ESG practices are more likely to be grouped together. The significance of these ESG factors indicates that sustainable practices are not only important for individual company performance but also play a crucial role in the broader market dynamics and community structures within financial networks.

Overall, the integration of network community analysis and nonparametric test findings highlights the interplay between sectoral affiliation and ESG practices in determining stock price correlations. The distinct communities formed within the manufacturing and financial sectors, driven by strong internal correlations, reflect the shared market influences and sectoral trends.

Table 7 displays the outcomes of nonparametric tests conducted on ESG scores across continuous mutual information network communities.

The nonparametric test results for ESG scores over continuous mutual information network communities, as presented in Table 7 , offer insightful findings. The tests reveal mixed significance levels across different ESG dimensions and community detection methods, shedding light on the nuanced impact of sustainability metrics on network clustering.

For the Leading Eigenvector method, the Kruskal–Wallis test indicates that none of the ESG dimensions, including Emission, Resource Use, Innovation, Human Rights, Product Responsibility, Workforce, Community, Management, Shareholders, and CSR Strategy, show significant differences between communities (all p -values > 0.05). This suggests that ESG scores do not substantially influence the formation of communities when using this method. Similarly, the Conover and log-rank tests do not show any significant results, reinforcing the lack of substantial impact of ESG scores on community structure in this context.

Conversely, the Girvan–Newman method reveals significant results for several ESG dimensions. The Kruskal–Wallis test shows that Emission ( \(p=0.032\) ) and CSR Strategy ( \(p=0.07\) ) have lower p -values, indicating potential significance. The Conover test highlights no significant differences, while the log-rank test identifies Emission ( \(p=0.034\) ), Innovation ( \(p=0.021\) ), and CSR Strategy ( \(p=0.065\) ) as significantly influencing the clustering of companies. These findings suggest that certain ESG scores, particularly Emission, Innovation, and CSR Strategy, play a more pronounced role in defining community structures within the Girvan–Newman-derived networks.

In the continuous mutual information network, the Girvan–Newman algorithm reveals that Community 1 predominantly consists of diverse sector companies, indicating a broad mix influenced by various ESG factors. However, Community 2 includes key financial and commercial companies, which are likely influenced by strong governance and corporate responsibility practices. Community 3 and Community 4, which display a blend of manufacturing and technology sectors, suggest that companies within these sectors share similar innovation and resource use strategies, aligning with their clustering patterns.

Findings highlight how sustainability metrics, such as Emissions and CSR Strategies, play a critical role in shaping network topology, particularly in the continuous mutual information network. Companies with high scores in these ESG areas tend to form distinct clusters, emphasizing the importance of shared sustainability practices. This clustering not only reflects similar market behaviours but also underscores the systemic impact of ESG performance on financial networks.

Table 8 displays the outcomes of nonparametric tests conducted on ESG scores across discrete bivariate mutual information network communities.

The nonparametric test results from Table 8 for ESG scores over discrete bivariate mutual information network communities present several notable insights.

For the Leading Eigenvector method, significant p -values were observed for CSR Strategy in both the Kruskal–Wallis and log-rank tests, indicating a substantial impact of CSR Strategy scores on community formation. This suggests that companies with similar CSR strategies are more likely to cluster together, reflecting shared commitments to corporate social responsibility and potentially similar operational practices. Additionally, Resource Use showed significance in the Conover test, pointing towards its role in influencing how companies group within the network. In the Girvan–Newman method, only community is significant according to the Conover test, reinforcing its importance for community clustering.

Hence, companies with higher resource efficiency and stronger corporate social responsibility practices tend to cluster together, reflecting shared sustainability priorities. For instance, companies like BIZIM and MGROS, which show significant values in these ESG categories, form part of the same community, emphasizing their alignment in sustainability practices.

ESG test results thus complement the community structures observed in the discrete bivariate mutual information network. Companies with similar ESG scores, particularly in Resource Use and CSR Strategy, tend to form distinct clusters, underscoring the influence of sustainability practices on their stock price interrelations. This alignment suggests that shared ESG goals and operational practices drive the formation of these communities, reflecting the interconnectedness of sustainability performance and financial behaviour. The significant ESG factors highlight key areas where company sustainability practices are most impactful, shaping the network topology and providing insights into drivers of sustainable investment.

Table 9 presents the results of nonparametric tests for ESG scores across linear causality network communities, highlighting significant findings for various sustainability metrics.

The nonparametric test results presented in Table 9 for ESG scores over the linear causality network communities reveal some significant findings, particularly for the Leading Eigenvector method. Notably, the Kruskal–Wallis test shows significant results for Human Rights ( \(p=0.012\) ), indicating that there is a meaningful difference in the Human Rights scores across different communities. This is further supported by the Conover test ( \(p=0.003\) ) and the log-rank test ( \(p=0.022\) ), which also show significant differences, suggesting that companies with similar Human Rights scores tend to cluster together more tightly in the network. This finding implies that HR practices are a critical factor influencing the formation of communities within the linear causality network.

Additionally, the log-rank test reveals significant results for Emission ( \(p=0.034\) ) and Innovation ( \(p=0.02\) ) scores in the Girvan–Newman method, indicating that these ESG metrics also play a substantial role in how companies cluster. This suggests that companies with similar Emission and Innovation scores are more likely to form communities, reflecting shared sustainability practices and innovation strategies.

Results highlight that specific ESG scores, particularly Human Rights, Emission, and Innovation, significantly impact the clustering of companies within the linear causality network.

Communities 3–5, which include a mix of sectors, indicate the presence of significant inter-sector dependencies. This is reflected in the significant Kruskal–Wallis test results for Human Rights under the Leading Eigenvector method, suggesting that companies with similar Human Rights scores tend to cluster together. This clustering could be driven by shared practices and policies that transcend sector boundaries, indicating that human rights practices are crucial in forming these inter-sectoral links. Community 6, which shows notable interactions within the energy sector, aligns with the significant results for Emission scores under the Girvan–Newman method. This suggests that companies within the energy sector with similar Emission scores are more likely to form clusters, reflecting common environmental practices and regulatory influences.

The Girvan–Newman method identifies seven communities with a structure that emphasizes both intra- and inter-sector dependencies. The significant results for Innovation scores indicate that companies with similar innovation practices are likely to cluster together, regardless of their sector. This suggests that innovation is a key factor in forming causal connections within the network, with companies sharing similar Innovation scores showing predictive stock price movements. Additionally, the Conover test results for community scores under the Leading Eigenvector method highlight the importance of community engagement and social responsibility in shaping network communities. Companies with strong community engagement practices are likely to be interconnected within the same community, driven by shared social goals and responsibilities.

Table 10 displays the outcomes of nonparametric tests conducted on ESG scores across nonlinear causality network communities.

The nonparametric test results presented in Table 10 for ESG scores over nonlinear causality network communities provide valuable insights into how specific sustainability metrics influence the clustering of companies.

For the Leading Eigenvector method, several ESG scores show significant impacts on community formation. The Kruskal–Wallis test indicates that Innovation ( \(p=0.019\) ), Human Rights ( \(p=0.02\) ), and Emission ( \(p=0.074\) ) scores significantly affect community structure. These results suggest that companies with similar innovation capabilities, human rights practices, and emission policies are more likely to cluster together. The Conover test further supports the influence of Human Rights ( \(p=0.073\) ) and Workforce ( \(p=0.17\) ) on community formation, although it shows slightly different significance levels. The log-rank test reveals significant impacts for Emission ( \(p=0.056\) ), Resource Use ( \(p=0.045\) ), Innovation ( \(p=0.02\) 2), and Human Rights ( \(p=0.038\) ), emphasizing the role of environmental and social governance factors in driving network clustering.

The Girvan–Newman results align with these findings to some extent but also present unique insights. The Kruskal–Wallis test highlights the significant impact of Human Rights ( \(p=0.057\) ) and Shareholders ( \(p=0.081\) ), suggesting that these factors are crucial in determining how companies group within the network. According to the Conover test, Product Responsibility ( \(p=0.013\) ) and Workforce ( \(p=0.079\) ) had a significant impact. The log-rank test underscores the importance of Human Rights ( \(p=0.023\) ) and Shareholders ( \(p=0.059\) ), suggesting that companies with similar practices in these areas tend to form tighter-knit communities.

The nonparametric test results for ESG scores over nonlinear causality network communities reveal critical insights into the role of sustainability metrics in influencing company clustering. Financial companies such as AKBNK and GARAN, which are central in Community 1, highlight the importance of the Emission and Human Rights scores in community formation. The log-rank test shows significant results for Emission and Human Rights within the Leading Eigenvector method. This suggests that companies with lower emissions and strong human rights policies are more likely to cluster together, reflecting shared sustainability practices that influence their stock price movements.

Similarly, Community 2, which features manufacturing giants like TOASO and VESTL, shows the impact of Innovation and Human Rights scores on clustering. The Kruskal–Wallis test for Innovation and Human Rights indicates that companies excelling in these areas form tighter communities, driven by shared innovative practices and robust human rights policies. This emphasizes the role of ESG factors in shaping sector-specific causal relationships.

The diverse sectoral mix in Communities 3–5 suggests significant inter-sector dependencies, which are influenced by ESG scores. The Conover test for Management within the Leading Eigenvector method highlights that strong management practices are critical for inter-sectoral clustering. This shows that companies with effective management strategies, regardless of their sector, tend to form communities with interconnected stock price movements.

The energy sector’s notable interactions in Community 6 align with significant log-rank test results for Resource Use and Innovation. These findings indicate that companies with efficient resource use and innovative practices within the energy sector form strong causal links, reflecting shared operational efficiencies and sustainable practices.

Conclusions

This study aimed to investigate the clustering behaviour of companies within different network models based on daily closing prices and examine the influence of ESG scores on these clusters. By applying various network analysis methods (i.e., correlation networks, continuous and discrete mutual information networks, linear and nonlinear causality networks), we effectively captured the complex interdependencies and interactions among companies. The nonparametric tests performed on ESG scores allowed us to assess the impact of sustainability metrics on community formation, fulfilling the primary objective of understanding how ESG factors shape financial networks.

The comparison of different network models revealed distinct and multifaceted patterns of interconnectivity among companies, offering a comprehensive view of market dynamics. The correlation networks underscored strong sectoral linkages, particularly within the financial and manufacturing sectors. This suggests that companies within these sectors exhibit similar stock price movements, likely driven by sector-specific factors and market conditions. Continuous mutual information networks provided deeper insights into both intra- and inter-sector dependencies, reflecting more nuanced informational relationships that go beyond simple linear correlations. These networks highlighted how certain sectors are interconnected through shared information flows, revealing a complex web of market interactions.

Discrete mutual information networks emphasized the importance of specific informational exchanges between companies. This model illustrated how discrete events or data points can drive connectivity, showcasing the critical role of individual company actions and announcements in shaping market linkages. On the other hand, linear causality networks demonstrated how stock price movements are predictive of each other, capturing the directional influences and temporal dependencies within the market. This approach highlighted the causal pathways through which market shocks or trends propagate across different companies and sectors.

Nonlinear causality networks expanded this perspective by capturing more complex, nonlinear relationships that may not be evident through linear models. This method revealed hidden dependencies and intricate feedback loops within the market, underscoring the rich and dynamic nature of financial interactions. Collectively, diverse network perspectives underscored the varying degrees of connectivity and influence within the financial market, illustrating the complexity and richness of market dynamics. By integrating multiple models, we obtained a holistic understanding of how companies are interlinked, the role of sectoral affiliations, and the intricate web of causal relationships that drive market behaviour.

The community detection results across different network models consistently highlighted the significant role of sectoral affiliation in forming clusters. The Leading Eigenvector and Girvan–Newman methods both revealed that companies within the same sector, such as financial and manufacturing firms, formed tight-knit communities. This indicates strong intra-sector relationships driven by shared market behaviours and sector-specific factors. The robustness of these methods in identifying sectoral clusters demonstrates their effectiveness in capturing the underlying structure of market networks.

In correlation networks, the financial and manufacturing sectors prominently formed distinct communities, reflecting the high degree of correlation within these sectors. This pattern indicates that companies within these sectors exhibit similar stock price movements, likely influenced by common economic drivers and market conditions. Sector-specific clusters provide valuable insights into how market participants within the same industry are interconnected.

The continuous mutual information networks further emphasized the importance of sectoral clustering, while also revealing significant inter-sector dependencies. Mixed-sector communities identified in these networks highlight how different industries are interlinked through shared informational relationships. For instance, financial and commercial companies forming a single community suggest that these sectors may be influenced by common external factors, leading to shared market behaviours.

Discrete mutual information networks showed specific informational exchanges between companies, illustrating how discrete events or data points can drive clustering. This approach highlighted the critical role of individual company actions in shaping network structures, with sectoral affiliations still playing a key role in forming communities.

Linear and nonlinear causality networks captured the directional and complex relationships between companies. Such networks showed that company stock price movements can predict each other, reinforcing the importance of causal influences in market dynamics. Clustering results from these models revealed strong internal causal influences within sectors like financial and manufacturing, while also showing cross-sectoral causal connections.

Overall, the robust clustering patterns observed across different methods underscore their effectiveness in identifying meaningful community structures. These results provide valuable insights into the underlying drivers of market connectivity, highlighting the importance of both intra-sector relationships and inter-sector dependencies in shaping the financial network topology. By understanding community structures, we can better grasp the dynamics of market behaviours and factors driving company interconnectivity.

The nonparametric test results for ESG scores revealed significant insights into the role of sustainability metrics in community formation within financial networks. Notably, ESG factors such as emission, CSR strategy, innovation, and human rights emerged as significant influence variables in different network models. For instance, in the Girvan–Newman method applied to nonlinear causality network, significant results for Emission and CSR Strategy highlighted their impact on clustering. Findings suggest that companies with strong performance in these ESG areas tend to form more cohesive communities, reflecting shared sustainability practices and priorities. Companies with lower emissions or more robust CSR strategies are more likely to be interconnected within the same community, driven by common goals and operational practices related to sustainability. This underscores the critical role of ESG factors in shaping financial networks and promoting sustainable investment practices.

In the continuous mutual information network, ESG factors such as Human Rights and Innovation showed significant p -values, indicating their substantial impact on community structure. Companies excelling in human rights practices or innovation tend to cluster together, suggesting that these aspects of ESG performance foster strong informational linkages and shared market behaviours. Similarly, the linear causality network revealed significant results for ESG scores like Human Rights and Management, highlighting how companies with strong governance and social responsibility practices influence market connectivity.

The discrete bivariate mutual information network also emphasized the importance of specific ESG factors. Significant results for product responsibility and shareholders indicated that these aspects of sustainability play crucial roles in forming community structures. Companies with high scores in product responsibility tend to cluster together, reflecting their commitment to quality and ethical business practices. This clustering based on shared sustainability priorities reinforces the idea that ESG performance drives market behaviours and intercompany relationships.

Overall, findings across different network models and community detection methods demonstrate the multifaceted impact of ESG factors on financial networks. They highlight how sustainability metrics not only influence individual company performance but also shape broader market dynamics by fostering interconnected, cohesive communities of companies with similar ESG practices. This reinforces the importance of integrating ESG considerations into investment decisions to promote sustainable and responsible financial markets.

Despite the comprehensive analysis, this study has several limitations. Firstly, the reliance on daily closing prices may not capture all market dynamics and intra-day variations. Additionally, the ESG scores used were limited to publicly available data, which may not fully represent the companies’ overall sustainability performance. The static nature of network models also does not account for temporal changes in company relationships and market conditions. Furthermore, the study focused on a specific set of companies within the Borsa Istanbul Sustainability Index, which may limit the generalizability of findings to other markets or indices. Finally, the nonparametric tests (while robust) may not fully capture the complex interactions between ESG factors and network communities.

Future research could address these limitations by incorporating intra-day trading data to capture more granular market dynamics and provide a more detailed understanding of company interdependencies. Expanding the dataset to include a broader range of companies and multiple stock indices could enhance the generalizability of findings. Additionally, longitudinal studies that track the evolution of network structures and community formations over time would provide valuable insights into temporal changes and the impact of external events on market connectivity.

Investigating the impact of different types of ESG scores, such as those derived from third-party assessments or alternative data sources like social media sentiment, could offer a more comprehensive view of sustainability practices. Furthermore, integrating machine learning techniques to dynamically adjust network models based on changing market conditions could enhance the robustness and predictive power of the analysis.

Exploring the interactions between ESG scores and other financial metrics, such as volatility or liquidity, could provide a deeper understanding of how sustainability influences broader market behaviours. Additionally, examining the role of regulatory changes and policy interventions on ESG-driven clustering could inform policymakers and investors about the effectiveness of sustainability regulations.

Conducting cross-market comparisons to assess how ESG factors influence network structures in different economic contexts could yield valuable insights into the global applicability of the findings. Finally, developing real-time monitoring tools based on network analysis and ESG metrics could help investors make informed decisions and promote sustainable investment practices.

In conclusion, this study highlights the intricate relationships between ESG factors and financial network structures, demonstrating the significant impact of sustainability metrics on market connectivity. The application of various network models and nonparametric tests provided a comprehensive understanding of how companies cluster based on their financial performance and sustainability practices. These findings underscore the importance of integrating ESG considerations into financial analysis, paving the way for more sustainable and informed investment strategies. As we move forward, embracing advanced analytical techniques and expanding the scope of research will further enhance our understanding of the complex interplay between sustainability and market dynamics, ultimately contributing to the development of more resilient and sustainable financial systems.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Batrancea, L.M., Akgüller, Ö., Balcı, M.A. et al. Financial network communities and methodological insights: a case study for Borsa Istanbul Sustainability Index. Humanit Soc Sci Commun 11 , 1046 (2024). https://doi.org/10.1057/s41599-024-03527-y

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