## Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

## Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

## Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

## Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

## Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

- It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
- It can be used in almost all fields from mathematics to physics to psychology and so on.
- It is easy to understand for its visual impacts.
- It shows the whole and huge data in an instance.
- It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

## Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

- Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
- Measurement Unit: The measurement unit in the graph should be mentioned.
- Proper Scale: A proper scale needs to be chosen to represent the data accurately.
- Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
- Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
- Simple: The construction of a graph should be easily understood.
- Neat: The graph should be visually neat in terms of size and font to read the data accurately.

## Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

## Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

## Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

- x and y graph
- Frequency Polygon
- Cumulative Frequency

## Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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## Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

## What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

- Stem and leaf plot
- Scatter diagrams
- Frequency Distribution

## Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

## What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

## What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

## What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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## 17 Data Visualization Techniques All Professionals Should Know

- 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

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## What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

## Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

- Gantt Chart
- Box and Whisker Plot
- Waterfall Chart
- Scatter Plot
- Pictogram Chart
- Highlight Table
- Bullet Graph
- Choropleth Map
- Network Diagram
- Correlation Matrices

## 1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

## 2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

## 3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

## 4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

## 5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

## 6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

## 7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

## 8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

## 9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

## 10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

## 11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

## 12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

## 13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

## 14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

## 15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

## 16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

## 17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

## Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

- Bubble clouds
- Circle views
- Dendrograms
- Dot distribution maps
- Open-high-low-close charts
- Polar areas
- Radial trees
- Ring Charts
- Sankey diagram
- Span charts
- Streamgraphs
- Wedge stack graphs
- Violin plots

## Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

## Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

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## Graphical Methods – Types, Examples and Guide

Table of Contents

## Graphical Methods

Definition:

Graphical methods refer to techniques used to visually represent data, relationships, or processes using charts, graphs, diagrams, or other graphical formats. These methods are widely used in various fields such as science, engineering, business, and social sciences, among others, to analyze, interpret and communicate complex information in a concise and understandable way.

## Types of Graphical Methods

Here are some of the most common types of graphical methods for data analysis and visual presentation:

## Line Graphs

These are commonly used to show trends over time, such as the stock prices of a particular company or the temperature over a certain period. They consist of a series of data points connected by a line that shows the trend of the data over time. Line graphs are useful for identifying patterns in data, such as seasonal changes or long-term trends.

These are commonly used to compare values of different categories, such as sales figures for different products or the number of students in different grade levels. Bar charts use bars that are either horizontal or vertical and represent the data values. They are useful for comparing data visually and identifying differences between categories.

These are used to show how a whole is divided into parts, such as the percentage of students in a school who are enrolled in different programs. Pie charts use a circle that is divided into sectors, with each sector representing a portion of the whole. They are useful for showing proportions and identifying which parts of a whole are larger or smaller.

## Scatter Plots

These are used to visualize the relationship between two variables, such as the correlation between a person’s height and weight. Scatter plots consist of a series of data points that are plotted on a graph and connected by a line or curve. They are useful for identifying trends and relationships between variables.

These are used to show the distribution of data across a two-dimensional plane, such as a map of a city showing the density of population in different areas. Heat maps use color-coded cells to represent different levels of data, with darker colors indicating higher values. They are useful for identifying areas of high or low density and for highlighting patterns in data.

These are used to show the distribution of data in a single variable, such as the distribution of ages of a group of people. Histograms use bars that represent the frequency of each data value, with taller bars indicating a higher frequency. They are useful for identifying the shape of a distribution and for identifying outliers or unusual data values.

## Network Diagrams

These are used to show the relationships between different entities or nodes, such as the relationships between people in a social network. Network diagrams consist of nodes that are connected by lines that represent the relationship. They are useful for identifying patterns in complex data and for understanding the structure of a network.

Box plots, also known as box-and-whisker plots, are a type of graphical method used to show the distribution of data in a single variable. They consist of a box with whiskers extending from the top and bottom of the box. The box represents the middle 50% of the data, with the median value indicated by a line inside the box. The whiskers represent the range of the data, with any data points outside the whiskers indicated as outliers. Box plots are useful for identifying the spread and shape of a distribution and for identifying outliers or unusual data values.

## Applications of Graphical Methods

Graphical methods have a wide range of applications in various fields, including:

- Business : Graphical methods are commonly used in business to analyze sales data, financial data, and other types of data. They are useful for identifying trends, patterns, and outliers, as well as for presenting data in a clear and concise manner to stakeholders.
- Science and engineering: Graphical methods are used extensively in scientific and engineering fields to analyze data and to present research findings. They are useful for visualizing complex data sets and for identifying relationships between variables.
- Social sciences: Graphical methods are used in social sciences to analyze and present data related to human behavior, such as demographics, survey results, and statistical analyses. They are useful for identifying trends and patterns in large data sets and for communicating findings to a broader audience.
- Education : Graphical methods are used in education to present information to students and to help them understand complex concepts. They are useful for visualizing data and for presenting information in a way that is easy to understand.
- Healthcare : Graphical methods are used in healthcare to analyze patient data, to track disease outbreaks, and to present medical information to patients. They are useful for identifying patterns and trends in patient data and for communicating medical information in a clear and concise manner.
- Sports : Graphical methods are used in sports to analyze and present data related to player performance, team statistics, and game outcomes. They are useful for identifying trends and patterns in player and team data and for communicating this information to coaches, players, and fans.

## Examples of Graphical Methods

Here are some examples of real-time applications of graphical methods:

- Stock Market: Line graphs, candlestick charts, and bar charts are widely used in real-time trading systems to display stock prices and trends over time. Traders use these charts to analyze historical data and make informed decisions about buying and selling stocks in real-time.
- Weather Forecasting : Heat maps and radar maps are commonly used in weather forecasting to display current weather conditions and to predict future weather patterns. These maps are useful for tracking the movement of storms, identifying areas of high and low pressure, and predicting the likelihood of severe weather events.
- Social Media Analytics: Scatter plots and network diagrams are commonly used in social media analytics to track the spread of information across social networks. Analysts use these graphs to identify patterns in user behavior, to track the popularity of specific topics or hashtags, and to monitor the influence of key opinion leaders.
- Traffic Analysis: Heat maps and network diagrams are used in traffic analysis to visualize traffic flow patterns and to identify areas of congestion or accidents. These graphs are useful for predicting traffic patterns, optimizing traffic flow, and improving transportation infrastructure.
- Medical Diagnostics: Box plots and histograms are commonly used in medical diagnostics to display the distribution of patient data, such as blood pressure, heart rate, or blood sugar levels. These graphs are useful for identifying patterns in patient data, diagnosing medical conditions, and monitoring the effectiveness of treatments in real-time.
- Cybersecurity: Heat maps and network diagrams are used in cybersecurity to visualize network traffic patterns and to identify potential security threats. These graphs are useful for identifying anomalies in network traffic, detecting and mitigating cyber attacks, and improving network security protocols.

## How to use Graphical Methods

Here are some general steps to follow when using graphical methods to analyze and present data:

- Identify the research question: Before creating any graphs, it’s important to identify the research question or hypothesis you want to explore. This will help you select the appropriate type of graph and ensure that the data you collect is relevant to your research question.
- Collect and organize the data: Collect the data you need to answer your research question and organize it in a way that makes it easy to work with. This may involve sorting, filtering, or cleaning the data to ensure that it is accurate and relevant.
- Select the appropriate graph : There are many different types of graphs available, each with its own strengths and weaknesses. Select the appropriate graph based on the type of data you have and the research question you are exploring. For example, a scatterplot may be appropriate for exploring the relationship between two continuous variables, while a bar chart may be appropriate for comparing categorical data.
- Create the graph: Once you have selected the appropriate graph, create it using software or a tool that allows you to customize the graph based on your needs. Be sure to include appropriate labels and titles, and ensure that the graph is clearly legible.
- Analyze the graph: Once you have created the graph, analyze it to identify patterns, trends, and relationships in the data. Look for outliers or other anomalies that may require further investigation.
- Draw conclusions: Based on your analysis of the graph, draw conclusions about the research question you are exploring. Use the graph to support your conclusions and to communicate your findings to others.
- Iterate and refine: Finally, refine your graph or create additional graphs as needed to further explore your research question. Iteratively refining and revising your graphs can help to ensure that you are accurately representing the data and that you are drawing the appropriate conclusions.

## When to use Graphical Methods

Graphical methods can be used in a variety of situations to help analyze, interpret, and communicate data. Here are some general guidelines on when to use graphical methods:

- To identify patterns and trends: Graphical methods are useful for identifying patterns and trends in data, which may be difficult to see in raw data tables or spreadsheets. Graphs can reveal trends that may not be immediately apparent in the data, making it easier to draw conclusions and make predictions.
- To compare data: Graphs can be used to compare data from different sources or over different time periods. Graphical comparisons can make it easier to identify differences or similarities in the data, which can be useful for making decisions and taking action.
- To summarize data : Graphs can be used to summarize large amounts of data in a single visual display. This can be particularly useful when presenting data to a broad audience, as it can help to simplify complex data sets and make them more accessible.
- To communicate data: Graphs can be used to communicate data and findings to a variety of audiences, including stakeholders, colleagues, and the general public. Graphs can be particularly useful in situations where data needs to be presented quickly and in a way that is easy to understand.
- To identify outliers: Graphical methods are useful for identifying outliers or anomalies in the data. Outliers can be indicative of errors or unusual events, and may warrant further investigation.

## Purpose of Graphical Methods

The purpose of graphical methods is to help people analyze, interpret, and communicate data in a way that is both accurate and understandable. Graphical methods provide visual representations of data that can be easier to interpret than tables of numbers or raw data sets. Graphical methods help to reveal patterns and trends that may not be immediately apparent in the data, making it easier to draw conclusions and make predictions. They can also help to identify outliers or unusual data points that may warrant further investigation.

In addition to helping people analyze and interpret data, graphical methods also serve an important communication function. Graphs can be used to present data to a wide range of audiences, including stakeholders, colleagues, and the general public. Graphs can help to simplify complex data sets, making them more accessible and easier to understand. By presenting data in a clear and concise way, graphical methods can help people make informed decisions and take action based on the data.

Overall, the purpose of graphical methods is to provide a powerful tool for analyzing, interpreting, and communicating data. Graphical methods help people to better understand the data they are working with, to identify patterns and trends, and to make informed decisions based on the data.

## Characteristics of Graphical Methods

Here are some characteristics of graphical methods:

- Visual Representation: Graphical methods provide a visual representation of data, which can be easier to interpret than tables of numbers or raw data sets. Graphs can help to reveal patterns and trends that may not be immediately apparent in the data.
- Simplicity : Graphical methods simplify complex data sets, making them more accessible and easier to understand. By presenting data in a clear and concise way, graphical methods can help people make informed decisions and take action based on the data.
- Comparability : Graphical methods can be used to compare data from different sources or over different time periods. This can help to identify differences or similarities in the data, which can be useful for making decisions and taking action.
- Flexibility : Graphical methods can be adapted to different types of data, including continuous, categorical, and ordinal data. Different types of graphs can be used to display different types of data, depending on the characteristics of the data and the research question.
- Accuracy : Graphical methods should accurately represent the data being analyzed. Graphs should be properly scaled and labeled to avoid distorting the data or misleading viewers.
- Clarity : Graphical methods should be clear and easy to read. Graphs should be designed with the viewer in mind, using appropriate colors, labels, and titles to ensure that the message of the graph is conveyed effectively.

## Advantages of Graphical Methods

Graphical methods offer several advantages for analyzing and presenting data, including:

- Clear visualization: Graphical methods provide a clear and intuitive visual representation of data that can help people understand complex relationships, trends, and patterns in the data. This can be particularly useful when dealing with large and complex data sets.
- Efficient communication: Graphical methods can help to communicate complex data sets in an efficient and accessible way. Visual representations can be easier to understand than numerical data alone, and can help to convey key messages quickly.
- Effective comparison: Graphical methods allow for easy comparison between different data sets, making it easier to identify trends, patterns, and differences. This can help in making decisions, identifying areas for improvement, or developing new insights.
- Improved decision-making: Graphical methods can help to inform decision-making by presenting data in a clear and easy-to-understand format. They can also help to identify key areas of focus, enabling individuals or teams to make more informed decisions.
- Increased engagement: Graphical methods can help to engage audiences by presenting data in an engaging and interactive way. This can be particularly useful in presentations or reports, where visual representations can help to maintain audience attention and interest.
- Better understanding: Graphical methods can help individuals to better understand the data they are working with, by providing a clear and intuitive visual representation of the data. This can lead to improved insights and decision-making, as well as better understanding of the implications of the data.

## Limitations of Graphical Methods

Here are a few limitations to consider:

- Misleading representation: Graphical methods can potentially misrepresent data if they are not designed properly. For example, inappropriate scaling or labeling of the axes or the use of certain types of graphs can create a distorted view of the data.
- Limited scope: Graphical methods can only display a limited amount of data, which can make it difficult to capture the full complexity of a data set. Additionally, some types of data may be difficult to represent visually.
- Time-consuming : Creating graphs can be a time-consuming process, particularly if multiple graphs need to be created and analyzed. This can be a limitation in situations where time is limited or resources are scarce.
- Technical skills: Some graphical methods require technical skills to create and interpret. For example, certain types of graphs may require knowledge of specialized software or programming languages.
- Interpretation : Interpreting graphs can be subjective, and the same graph can be interpreted in different ways by different people. This can lead to confusion or disagreements when using graphs to communicate data.
- Accessibility : Some graphical methods may not be accessible to all audiences, particularly those with visual impairments. Additionally, some types of graphs may not be accessible to those with limited literacy or numeracy skills.

## About the author

## Muhammad Hassan

Researcher, Academic Writer, Web developer

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## Graphical Representation

Graphical representation definition.

Graphical representation refers to the use of charts and graphs to visually display, analyze, clarify, and interpret numerical data, functions, and other qualitative structures.

## What is Graphical Representation?

Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone.

Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.

## Types of Graphical Representation

Data charts are available in a wide variety of maps, diagrams, and graphs that typically include textual titles and legends to denote the purpose, measurement units, and variables of the chart. Choosing the most appropriate chart depends on a variety of different factors -- the nature of the data, the purpose of the chart, and whether a graphical representation of qualitative data or a graphical representation of quantitative data is being depicted. There are dozens of different formats for graphical representation of data. Some of the most popular charts include:

- Bar Graph -- contains a vertical axis and horizontal axis and displays data as rectangular bars with lengths proportional to the values that they represent; a useful visual aid for marketing purposes
- Choropleth -- thematic map in which an aggregate summary of a geographic characteristic within an area is represented by patterns of shading proportionate to a statistical variable
- Flow Chart -- diagram that depicts a workflow graphical representation with the use of arrows and geometric shapes; a useful visual aid for business and finance purposes
- Heatmap -- a colored, two-dimensional matrix of cells in which each cell represents a grouping of data and each cell’s color indicates its relative value
- Histogram – frequency distribution and graphical representation uses adjacent vertical bars erected over discrete intervals to represent the data frequency within a given interval; a useful visual aid for meteorology and environment purposes
- Line Graph – displays continuous data; ideal for predicting future events over time; a useful visual aid for marketing purposes
- Pie Chart -- shows percentage values as a slice of pie; a useful visual aid for marketing purposes
- Pointmap -- CAD & GIS contract mapping and drafting solution that visualizes the location of data on a map by plotting geographic latitude and longitude data
- Scatter plot -- a diagram that shows the relationship between two sets of data, where each dot represents individual pieces of data and each axis represents a quantitative measure
- Stacked Bar Graph -- a graph in which each bar is segmented into parts, with the entire bar representing the whole, and each segment representing different categories of that whole; a useful visual aid for political science and sociology purposes
- Timeline Chart -- a long bar labelled with dates paralleling it that display a list of events in chronological order, a useful visual aid for history charting purposes
- Tree Diagram -- a hierarchical genealogical tree that illustrates a family structure; a useful visual aid for history charting purposes
- Venn Diagram -- consists of multiple overlapping usually circles, each representing a set; the default inner join graphical representation

Proprietary and open source software for graphical representation of data is available in a wide variety of programming languages. Software packages often provide spreadsheets equipped with built-in charting functions.

## Advantages and Disadvantages of Graphical Representation of Data

Tabular and graphical representation of data are a vital component in analyzing and understanding large quantities of numerical data and the relationship between data points. Data visualization is one of the most fundamental approaches to data analysis, providing an intuitive and universal means to visualize, abstract, and share complex data patterns. The primary advantages of graphical representation of data are:

- Facilitates and improves learning: graphics make data easy to understand and eliminate language and literacy barriers
- Understanding content: visuals are more effective than text in human understanding
- Flexibility of use: graphical representation can be leveraged in nearly every field involving data
- Increases structured thinking: users can make quick, data-driven decisions at a glance with visual aids
- Supports creative, personalized reports for more engaging and stimulating visual presentations
- Improves communication: analyzing graphs that highlight relevant themes is significantly faster than reading through a descriptive report line by line
- Shows the whole picture: an instantaneous, full view of all variables, time frames, data behavior and relationships

Disadvantages of graphical representation of data typically concern the cost of human effort and resources, the process of selecting the most appropriate graphical and tabular representation of data, greater design complexity of visualizing data, and the potential for human bias.

## Why Graphical Representation of Data is Important

Graphic visual representation of information is a crucial component in understanding and identifying patterns and trends in the ever increasing flow of data. Graphical representation enables the quick analysis of large amounts of data at one time and can aid in making predictions and informed decisions. Data visualizations also make collaboration significantly more efficient by using familiar visual metaphors to illustrate relationships and highlight meaning, eliminating complex, long-winded explanations of an otherwise chaotic-looking array of figures.

Data only has value once its significance has been revealed and consumed, and its consumption is best facilitated with graphical representation tools that are designed with human cognition and perception in mind. Human visual processing is very efficient at detecting relationships and changes between sizes, shapes, colors, and quantities. Attempting to gain insight from numerical data alone, especially in big data instances in which there may be billions of rows of data, is exceedingly cumbersome and inefficient.

## Does HEAVY.AI Offer a Graphical Representation Solution?

HEAVY.AI's visual analytics platform is an interactive data visualization client that works seamlessly with server-side technologies HEAVY.AIDB and Render to enable data science analysts to easily visualize and instantly interact with massive datasets. Analysts can interact with conventional charts and data tables, as well as big data graphical representations such as massive-scale scatterplots and geo charts. Data visualization contributes to a broad range of use cases, including performance analysis in business and guiding research in academia.

- Math Article

## Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

- Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
- Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
- Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
- Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
- Frequency Table – The table shows the number of pieces of data that falls within the given interval.
- Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
- Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
- Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

## General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

- Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
- Measurement Unit: Mention the measurement unit in the graph.
- Proper Scale: To represent the data in an accurate manner, choose a proper scale.
- Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
- Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
- Keep it Simple: Construct a graph in an easy way that everyone can understand.
- Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

## Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem. There are two types of graphs to visually depict the information. They are:

- Time Series Graphs – Example: Line Graph
- Frequency Distribution Graphs – Example: Frequency Polygon Graph

## Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

- Smoothed frequency graph
- Pie diagram
- Cumulative or ogive frequency graph
- Frequency Polygon

## Merits of Using Graphs

Some of the merits of using graphs are as follows:

- The graph is easily understood by everyone without any prior knowledge.
- It saves time
- It allows us to relate and compare the data for different time periods
- It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

## Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

- Obtain the frequency distribution and find the midpoints of each class interval.
- Represent the midpoints along x-axis and frequencies along the y-axis.
- Plot the points corresponding to the frequency at each midpoint.
- Join these points, using lines in order.
- To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

## Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

- Line Graphs
- Frequency Table
- Circle Graph, etc.

Read More: Types of Graphs

## What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

- It makes data more easily understandable.
- It saves time.
- It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

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Why Graphics are Important in Application Development

Imagine opening a newly downloaded app and seeing a hastily put-together UI, a basic logo, a simple home screen, hard to read buttons, and no visual cues. You have to think about which path to follow.

On the other hand, you open an app with dazzling motion graphics, a striking colour palette, a beautifully designed home screen, an intuitive layout, and easy to follow commands with a minimal learning curve.

How would you feel about each app? Which app would you stick to? Which app are you more likely to recommend to your friends?

Ever wondered why users choose to download some apps over others that offer the same features and functionality? From a users’ perspective, the first reason has to be a great design.

Customers usually form an opinion about your app within the first few seconds, and compelling graphics allow you to make a great first impression and persuade people to download your app. This is because the first thing users usually notice is the graphical presentation of a mobile application.

So, the more eye-grabbing and aesthetically pleasant your app, the more eye-balls it will attract.

Terrific visuals make a user feel more comfortable with an app, which boosts engagement. Let’s explore why graphics are an integral part of application development.

Table of Contents

## Attract More Customers

People who say looks don’t matter will probably never download an app with below-par graphics. So, you may frown upon “beauty is only skin deep”, but you have to admit that presentable looks can help people forge a positive impression about anything, including mobile apps.

This means that you have to focus on the graphical design of your app to attract potential customers. If you succeed in developing a mobile app with great visuals, an eye-grabbing theme, popping imagery, an easy-to-follow layout with white open spaces , and intuitive navigation.

In that case, you will attract the users’ attention from the first go. Aesthetically pleasing, professionally designed graphics that resonate with users will help them stay in your mobile app as long as possible.

Well-thought-out graphics not only compel users to download an app themselves but also recommend it to others.

The ASOS shopping app features high-quality imagery with multi-coloured graphic elements against a white background, with the search bar, category navigation and menu items popping out.

The clutter-free, minimalistic graphics make the app highly user-friendly and engaging, ensuring that users can easily find an item they wish to buy, instead of getting distracted by clutter and an overwhelming layout.

## Stand out Amongst Competitors

With thousands of apps available on the Play Store and Apple store, with many similar to yours, it’s a cut-throat arena. Even if your app idea isn’t unique, aesthetic graphics may be the key to drawing attention and making your presence felt in the market.

Users will inevitably gravitate towards a customer-oriented, user-friendly option with a unique presence and grabbing visuals when presented with similar apps.

Great graphics stick in the minds of decision-makers long after they have interacted with a brand and can influence their choices.

For instance, even though there are hundreds of apps touting to help you better understand your spending habits, a new app, ‘joy’, is creating quite the hype.

The smooth onboarding process and an appealing modern and fresh design aesthetic make the app truly a joy to use. A bright colour palette and large, bold typography and conversational interface make the app cheerful and upbeat compared to the dull financial apps we are accustomed to.

## Offer Intuitive Functionality

Another important reason to highlight the role of graphics in mobile application development is to ensure your app delivers an intuitive user interface.

Remember that users seek a painless experience from brands . For instance, you want to make sure all the CTAs are conspicuous, stand out against the background, and are in places where you would intuitively reach for them.

This means that you want to simplify your users' navigation from the homepage to perform their desired actions in the least number of steps.

Remember that a decent UI and hassle-free user experience earn you a loyal customer base. In turn, satisfied users spread the word about your brand.

For instance, the “Let’s Fly” app is the classic definition of a no-nonsense, to-the-point, purpose-centred app that is oriented toward helping users find the most affordable flights to their desired destinations quickly and easily.

The app follows simple, easy-to-follow navigation that lets the users get down to business without getting sidetracked. While maintaining simplicity, efficiency, and functionality helps the app solve the users’ pain points quickly, colours and visuals break the monotony without taking away the focus from the task at hand.

## Cement your App Content

A picture is worth a thousand words. Where words fail, great visuals pick up. Whatever message you are trying to portray to your customers, aesthetic visuals summarise these ideas in a way that’s more relatable and easier to understand. Today's users may not have the time to read lengthy texts to convince them to purchase your product or use your app, but one compelling graphic will leave them hooked.

See how Vine stands out in the market by letting graphics take centre stage. Vine is a popular app for people wishing to record and share creative, memorable or humorous moments.

However, apart from its unique idea and stellar functionality, the app incorporates striking visual elements, such as adorable, functional icons for commenting, re-vining and liking individual posts, and beautifully designed illustrations punctuating content throughout the app.

Similarly, the Nice Weather app has become a popular go-to weather app for checking the temperature, wind speed and rainfall.

The minimal weather app uses simple visual elements crafted with white lines against a solid background to communicate all the information that you need to plan the day in a momentary glance.

## Convey A Sense of Professionalism

We cannot stress enough how great graphics affect the decision-making process. Ugly ducklings are ignored, no matter how well they deliver on the functional promises. Apps incorporating well-designed, high-quality graphics are perceived to be more trustworthy and high-functioning.

Graphics portray a sense of professionalism and authority that paves the path to the user’s heart. Research shows that most users are excited to use a well-designed app, more forgiving with bugs, and willing to spend more time learning its functionality.

Not to mention, great visuals make the content look more engaging and navigation less complicated, which results in a bevvy of satisfied customers.

Keeping tabs on your weekly expenses can be quite a drag, but look at how the fantastic app ‘Expense Manager’ helps you manage finances with great visuals.

The app leverages clearly defined colours to categorise your expenses and gives you an overview of your daily expenditures via pie charts and other easy-to-understand graphical representations. The gorgeous use of colours and graphics lends a highly professional appeal to the app.

## Tips to Pull Off an Exceptional Mobile App Design

Keep text legible and conspicuous.

All the text on your mobile app should be two things: readable and legible. If users cannot make out the text or even find it in the first place, there is no point in including any in the first place.

As a rule of thumb, aim for a font size above 16px and always use a clear, easy-to-read font type. Also, it is crucial to ensure ample contrast between the font and the background to make the text pop out. Light grey text against a white background may look classy, but users will have a field day deciphering your message. You can add accent colours to certain text parts to divert users' attention to it and help them retain the information presented.

Also, aim for 30 to 40 characters per line and ensure plenty of space between lines of text. Make sure users don’t have to pinch or zoom to read the text, as it would ruin the user experience.

## Use HD-Quality images

This one is a no-brainer, but make sure you only use the highest-quality images so they don’t appear pixelated on HD screens. Another factor to be mindful of is that your images appear in the perfect aspect ratio: neither stretched too broad nor too long.

Distorted images are highly unappealing. Also, image format counts. Instead of .gif, use .png as your preferred format since it gives you greater colour depth.

Furthermore, you should optimise your images and other graphics for fast loading speeds. Remember that most users do not have 4G, unlimited data plans, or access to fast coverage. This is why it is good design practice to keep all files small and compressed for ease of download.

Not to mention, files over 50 MB cannot be downloaded over 4G and need WIFI access. This situation is highly unfeasible for on-the-go apps usually run over 4G. A lag-free workflow will highly boost the experience for your users.

## Establish Hierarchy with colours

Using shades of the same colour establishes a sense of hierarchy, which intuitively moves your user along the path to accomplishing their goal or even denotes purpose. For instance, if one button is black, the next dark grey, and the third light grey, it shows that button 1 is the most important or denotes the first step, button 2 comes next, and button 3 comes last.

Similarly, colour associations can help you gently push users to take the action that you want or the most popular option available. For instance, when presented with a red and green button, most users click on the green button by default and avoid the red one without even reading the text.

Also, ensure high contrast in buttons to make them pop out against the background.

## Repeat Design elements throughout the App

Design elements can easily be repeated throughout your app. Start with defining the graphics elements and colour palette for your home screen, and then carry those visual cues through the rest of your app.

If one of the ‘next’ buttons is the colour orange, then all following buttons on the app should follow the same palette. If one CTA button has rounded edges, all the CTAs on your app should have rounded edges. If one screen has 10 px padding on all sides, all screens need to ensure the same. This eases the learning app and makes the app feel intuitive.

For instance, the eOxegen app is filled with carefree, likeable illustrated characters that appear at every crucial point of navigation and user journey and assist users in fulfilling their required actions.

Rounded fonts and flashy accent colours, and the use of colour to separate text modules are replicated throughout the app for a lighthearted, warm look. Design-wise, we see plenty of consistency throughout the app’s pages.

## Make sure your Graphics are Flexible.

Make sure your graphic elements are fluid enough to allow for rotating screens. Remember that mobile screens can rotate; unlike desktops, users can view screens in either the landscape or the portrait mode.

A fluid design looks good no matter which way it is viewed. Most graphic designers create separate versions of graphical elements for both the portrait and landscape view to ensuring they look good in every orientation.

## Don’t go overboard with graphics.

While graphics can significantly enhance the look and feel of your app, make sure that all the components in your app should be relevant and do not distract the user from the intended purpose.

A UI with too many colours, images, fonts and menus will be hard to navigate and lead to a sensory overload. UI should be intuitive and straightforward and allow the user to perform the necessary task accurately. Whenever you need to add graphics, make sure they contribute to the intent and make it easier for the user to use the app.

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## Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

## What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

## Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

- Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
- Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
- Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

## Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

- Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
- Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
- Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
- Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
- Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

## Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

- Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
- Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
- Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
- Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

## Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

- Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
- Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
- Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
- Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

## Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

- Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
- Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
- Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
- Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

## Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

## 1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

## 2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

## 3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

## 4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

## 5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

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## FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

## Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

## How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

## Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

## Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

## Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

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- Differences Between Stack and Queue Data Structures
- Breadth First Search vs Depth First Search
- What are Data Structures - Types of Data Structures (Complete Guide)
- Data Structures and Algorithms
- Recursion in Data Structures: Recursive Function
- Complexity Analysis of Data Structures and Algorithms
- Big O Notation in Data Structures: Time and Space Complexity
- Arrays in Data Structures - Types, Representation & Algorithm (With Examples)
- Types of Arrays in Data Structures: 2D, 3D, Jagged Arrays
- Doubly Linked List Algorithm in Data Structures with Examples
- LinkedList in Data Structures - Types of Linked Lists & Its Applications
- Implementing Stack in Data Structures
- Searching in Data Structures - Its Types, Methods & Techniques
- Queue in Data Structures - Types & Algorithm (With Example)
- Brute Force Algorithm in Data Structures: Types, Advantages, Disadvantages

## 03 Intermediate

- Binary Trees in Data Structures - Types, Implementation, Applications
- Circular Linked Lists in Data Structures
- Binary Search Tree in Data Structures
- What is Linear Search in Data Structures - Its Algorithm, Working, & Complexity
- Binary Search in Data Structures
- Sorting in Data Structures - Types of Sorting Algorithms ( With Examples )
- Bubble Sort in Data Structures
- Selection Sort in Data Structures
- Insertion Sort in Data Structures - Algorithm, Working, & Advantages
- Merge Sort in Data Structures and Algorithms: With Implementation in C++/Java/Python
- Quick Sort Algorithm in Data Structures - Its Types ( With Examples )
- Counting Sort in Data Structures
- Radix Sort in Data Structures - Its Algorithm, Working, & Complexity
- Bucket Sort in Data Structures
- Shell Sort in Data Structures - Algorithm, Visualization, & Complexity
- Divide and Conquer Algorithm in Data Structures - Its Working, Advantages & Disadvantages
- Greedy Algorithm in Data Structures

## 04 Advanced

- Heap in Data Structures
- Heap Sort Algorithm in Data Structures - Its Working, Implementation & Applications
- Hashing in Data Structures: Types and Functions [With Examples]
- Hash Table in Data Structures

## Graphs in Data Structures - Types of Graphs, Representation & Operations

- Breadth First Traversal and Depth First Traversal
- Spanning Tree and Minimum Spanning Tree in Data Structures - Kruskal's and Prim's Algorithms
- AVL Tree in Data Structures with Examples
- Trees in Data Structures - Its Structure, Operations & Applications
- Segment Tree in Data Structures: Operations, Advantages and Disadvantages
- Suffix Array and Suffix Tree in Data Structures & Applications
- K-Dimensional Tree in Data Structures
- Tower of Hanoi in Data Structures
- Bellman Ford’s Algorithm in Data Structures - Working, Example and Applications

## 05 Questions

- DSA Interview Questions and Answers (Freshers to Experienced)

## 06 Training Programs

- Java Programming Course
- C++ Programming Course
- Data Structures and Algorithms Training
- Datastructures
- Graphs In Data Structures..

## Data Structures & Algorithms Free Course

Graphs in data structures: an overview.

Graph in Data Structures is a type of non-primitive and non-linear data structure that consists of a finite set of nodes (or vertices) and a set of edges connecting them. In this DSA tutorial , we will see a detailed starting of the graph concept i.e. its features, types, implementation, etc. To further enhance your understanding and application of graph concepts, consider enrolling in the Dsa Course , where you can gain comprehensive insights into effective data structure utilization for improved problem-solving and time management.

## What is a Graph in Data Structures?

A graph is a collection of nodes that consist of data and are connected to other nodes of the graph. formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(V, E) .

The most common real-life examples of graphs are social media where a User, Photo, Album, Event, Group, Page, Comment, Story, Video, etc represents a node. Every relationship is an edge from one node to another. Whenever you post a photo, join a group, like a page, etc., a new edge is created for that relationship. Thus, it can be said that a social media platform is a collection of nodes and edges.

## Graph Terminologies in Data Structures

Graph terminology in data structure refers to the specific vocabulary and concepts used to describe and analyze graphs, which are mathematical structures composed of nodes (also called vertices) connected by edges.

- Node/Vertex: A fundamental unit of a graph. It represents an entity or an element and is usually depicted as a point.
- Edge/Arc: A connection between two nodes. It represents a relationship or a link between the corresponding entities. An edge can be directed (arc), indicating a one-way connection, or undirected, representing a two-way connection.
- Adjacent Nodes: Two nodes that are directly connected by an edge. In an undirected graph, both nodes are considered adjacent to each other. In a directed graph, adjacency depends on the direction of the edge.
- Degree: The degree of a node is the number of edges incident to it, i.e., the number of edges connected to that node. In a directed graph, the degree is divided into two categories: the in-degree (number of incoming edges) and the out-degree (number of outgoing edges).
- Path: A path in a graph is a sequence of edges that connects a sequence of nodes. It can be a simple path (no repeated nodes) or a closed path/cycle (starts and ends at the same node).
- Bipartite Graph: A graph whose nodes can be divided into two disjoint sets such that every edge connects a node from one set to a node from the other set. In other words, there are no edges between nodes within the same set.
- Spanning Tree: A subgraph of a connected graph that includes all the nodes of the original graph and forms a tree (a connected acyclic graph) by eliminating some of the edges.
- Cycle: A closed path in a graph, where the first and last nodes are the same. It consists of at least three edges.

Read More - Best Data Structure Interview Questions and Answers

## Types of Graphs in Data Structures

Finite graph.

If the graph, G=(V, E) has a finite number of edges and vertices, it is a finite graph. In other words, both the number of vertices and the number of edges in a finite graph are limited and can be counted.

## Infinite Graph

If the graph G=(V, E) has an infinite number of edges and vertices, it is an infinite graph.

## Trivial Graph

If a finite graph G=(V, E) has just one vertex and no edges, it is referred to as trivial. It is also known as a singleton graph or a single vertex graph.

## Simple Graph

A graph G=(V, E) is a simple one if each pair of nodes or vertices contains just one edge. In order to represent one-to-one interactions between two elements, there is only one edge connecting two vertices.

## Multi Graph

A graph G=(V, E) is referred to as a multigraph if it has some parallel edges between two vertices but doesn't contain any self-loop. An edge of a graph that starts from a vertex and ends at the same vertex is called a loop or a self-loop.

It's a revised version of a trivial graph. A graph G=(V, E) is a null graph if it has many vertices but none of them are connected by any edges. A null graph can also be referred to as an edgeless graph, an isolated graph, or a discrete graph.

## Complete Graph

A simple graph G=(V, E) with n vertices is also called a complete graph if the degree of each vertex is n-1, i.e. one vertex is attached with n-1 edges or the rest of the vertices in the graph. A complete graph is also called a Full Graph.

## Pseudo Graph

A pseudograph exists when a graph G= (V, E) contains some self-loop in addition to some multiple edges.

## Regular Graph

## Weighted Graph

A graph G=(V, E) in which edges have weights or costs associated with them is a weighted graph.

## Directed Graph

A directed graph, also known as a digraph, is a collection of nodes connected by edges, each with a distinct direction.

## Undirected Graph

A graph G=(V, E) in which edges have no direction, i.e., the edges do not have arrows indicating the direction of traversal is an undirected graph.

## Connected Graph

A graph G = (V, E) is said to be connected if there exists at least one path between each and every pair of vertices in the graph.

## Disconnected Graph

If in a graph G = (V, E), there does not exist any path between at least one pair of vertices, it is a disconnected graph. A null graph with n vertices is a disconnected graph.

## Cyclic Graph

A graph is termed cyclic if it forms at least one cycle.

## Acyclic Graph

A graph is said to be acyclic if it contains no cycles.

## Directed Acyclic Graph

It is a graph with directed edges but no cycle.

A subgraph is a set of vertices and edges in one graph that are subsets of another.

## Graph Representation in Data Structures

- Graph representation is a way of structuring and visualizing data using nodes (vertices) and edges. It is a technique to store graphs in the memory of a computer.
- In a graph, nodes represent individual entities, while edges represent the relationships or connections between those entities. The connections can be directional or undirected, depending on whether the edges have a specific direction or not.

There are two ways to represent a graph

## Adjacency Matrix

An Adjacency Matrix is a 2D array of size V x V where V is the number of nodes in a graph. It is used to represent a finite graph, with 0's and 1's. Since it's a V x V matrix, it is known as a square matrix. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph i.e. if there is any edge connecting a pair of nodes in the graph.

## Representation of Undirected Graph

## Representation of a Directed Graph

## Weighted Undirected Graph Representation

A weighted graph representing these values in the matrix is indicated at the graph's edge.

- Adjacency List

An adjacency list represents a graph as an array of linked lists . The index of the array represents a vertex and each element in its linked list represents the other vertices that form an edge with the vertex.

## Weighted Undirected Graph Representation Using Linked-List

## Weighted Undirected Graph Representation Using an Array

## Operations on Graphs in Data Structures

The following common operations are performed on graphs in data structures:

## Insert vertex

It is a simple addition of a vertex(node) in a graph. It need not be connected to any other vertex(node) through an edge.

## Delete vertex

To delete a nod, we also have to remove all the edges associated with that vertex.

## Insert Edge

It adds an edge between a pair of vertices.

## Delete Edge

An edge can be deleted by severing the link between its vertices or nodes. If all the edges from a particular vertex(node) are removed, then that vertex(node) becomes an isolated vertex.

## Graph Traversal

Graph traversal is the process of going through or updating each vertex in a graph. Such traversals are classified according to the order in which the algorithm visits the vertices. A subset of tree traversal is graph traversal.

There are two algorithms/ways to visit a graph:

- Breadth-first search
- Depth-first search

We will study all these two in the section Breadth First Traversal and Depth First Traversal

## Application of Graphs

- Maps GPS Systems can be represented using graphs and then can be used by computers to provide various services.
- When various tasks depend on each other, it can be represented using a Directed Acyclic graph and we can find the order in which tasks can be performed using topological sort.
- State Transition Diagram represents what can be the legal moves from current states.
- Graphs can be used to represent the topology of computer networks, such as the connections between routers and switches.

## Advantages of Graphs

- Graphs can be used to represent a wide range of relationships and data structures.
- They can be used to model and solve a wide range of problems, including pathfinding, data clustering, network analysis, and machine learning.
- Graph algorithms are often very efficient and can be used to solve complex problems quickly and effectively.
- They can be used to represent complex data structures simply and intuitively, making them easier to understand and analyze.

## Disadvantages of Graphs

- Graphs can be complex and difficult to understand, especially for people not familiar with graph theory or related algorithms.
- Creating and manipulating graphs can be computationally expensive, especially very large or complex graphs.
- Graph algorithms can be difficult to design and implement correctly and can be prone to bugs and errors.
- Graphs can be difficult to visualize and analyze, especially for very large or complex graphs, which can make it challenging to extract meaningful insights from the data.

So, here we saw a detailed introduction to graphs in data structures. You might have got at least some idea regarding graphs and their applications. We will cover all its aspects one by one in the upcoming tutorials. To also gain a practical understanding of graphs, enroll in our Best Dsa Course .

## Q1. What is a path in a graph?

Q2. what is meant by degree of a node in a graph, q3. what are the two ways to represent a graph.

- Adjacency Matrix

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## Graphical Representation of Sequences and Its Application

- First Online: 17 November 2023

## Cite this chapter

- Stephen S.-T. Yau 17 , 18 ,
- Xin Zhao 19 ,
- Kun Tian 20 &
- Hongyu Yu 21

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 58))

158 Accesses

Mathematical analysis of large-volume genomic DNA sequence data is one of the challenges for biologists. Graphical representation of DNA or protein sequences provides a simple way of viewing, sorting, and comparing sequence similarity. In this chapter, we introduce two directions to construct graphical representation for biological sequences. The first direction is by curves without degeneracy and the second one is by Chaos Game Representation.

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Stephen S.-T. Yau

Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, China

Beijing Electronic Science and Technology Institute, Beijing, China

Dept. of Mathematical Sciences, Renmin University of China, Beijing, China

Dept. of Mathematics, Tsinghua University, Beijing, China

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## About this chapter

Yau, S.ST., Zhao, X., Tian, K., Yu, H. (2023). Graphical Representation of Sequences and Its Application. In: Mathematical Principles in Bioinformatics. Interdisciplinary Applied Mathematics, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-031-48295-3_5

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WatElectronics.com

## Ladder Logic : Graphical Representation, Components, Example & Its Applications

November 24, 2023 By WatElectronics

The origins of Ladder Logic can be traced back to the world of relay-based control systems. In the early days of industrial automation, electrical engineers used relay circuits to control machinery. These circuits were represented graphically using ladder diagrams, where horizontal lines (rungs) represented power circuits, and vertical lines represented relay contacts and coils. As PLCs emerged to replace traditional relay systems, the graphical representation of ladder diagrams seamlessly transitioned into Ladder Logic programming. This visual language made it easier for engineers and electricians to understand and transition from traditional relay control to the digital realm of PLCs. In this article, we will explore the intricacies of Ladder Logic , its key features, application scenarios, and its enduring relevance in the ever-advancing landscape of industrial automation.

## Graphical Representation of Ladder Logic:

Ladder Logic gets its name from the characteristic graphical representation that resembles a ladder. The programming environment displays a series of horizontal lines (rungs), and each rung represents a specific control operation or sequence. The key elements of Ladder Logic include:

Ladder Logic

## Contacts (Switches):

Contacts represent input conditions or switches. They can be normally open (NO) or normally closed (NC), simulating the behavior of physical switches in an electrical circuit.

−−[]−−−−[]−−, where the brackets represent a normally open contact.

## Coils (Outputs):

Coils represent output actions or devices. They can be energized or de-energized based on the logical conditions in the contacts.

−−()−−−−()−− , where the parentheses represent a coil.

## Power Rails:

Power rails run vertically on either side of the ladder diagram and provide electrical power to the components on the rungs.

Example: ∣∣∣∣

Rungs are the horizontal lines that contain a series of contacts and coils. Each rung represents a unique control sequence.

Example: −−[]−−()−−−−[]−−()−−

## Key Features of Ladder Logic:

Intuitive design:.

Ladder Logic’s graphical representation is intuitive and closely mirrors traditional relay diagrams. This design makes it accessible to individuals with a background in electrical engineering.

## Sequential Execution:

The execution of this Logic programs is sequential, from left to right and top to bottom. This sequential nature makes it easy to follow the flow of logic and understand the program’s behavior.

## Discrete Logic Operations:

Ladder Logic excels at representing discrete logic operations such as AND, OR, and NOT. This makes it suitable for applications with discrete inputs and outputs, such as manufacturing processes and traffic control systems.

## Easy Debugging:

The graphical nature of this Logic facilitates easy debugging. Engineers can visually inspect ladder diagrams to identify faults or logical errors.

## Mimics Relay Logic:

Ladder Logic retains the conventions of traditional relay logic, making it a natural transition for those familiar with relay-based control systems.

## Components of Ladder Logic Programs:

Input Conditions (Contacts):

Ladder Logic programs begin with input conditions, represented by contacts. These conditions are typically sensors, switches, or other inputs that initiate the control sequence.

Logic Operations:

The body of the ladder diagram contains various logic operations, including AND, OR, and NOT. These operations determine the logical relationships between input conditions.

Output Actions (Coils):

The output actions, represented by coils, define the desired outcome based on the logic conditions. These can include activating motors, opening or closing valves, or triggering alarms.

Timers and Counters:

It supports the integration of timers and counters, allowing for the creation of time-based and count-based control sequences.

Branching and Jumping:

Conditional branching and jumping instructions enable the creation of more complex control structures within the sequential execution of the program.

## Applications of Ladder Logic:

Manufacturing Processes:

It is extensively used in manufacturing environments to control conveyor systems, assembly lines, and robotic processes. Its ability to represent sequential logic makes it well-suited for coordinating complex manufacturing operations.

Traffic Control Systems:

In traffic control systems, Ladder Logic can be employed to manage traffic lights and signals. The discrete nature of Ladder Logic aligns with the on/off behavior required for controlling traffic flow.

Packaging Machinery:

Packaging machines often utilize Ladder Logic to coordinate the precise movements of conveyors, sorting mechanisms, and packaging equipment. The graphical representation allows engineers to design and implement control logic with ease.

Water Treatment Plants:

It is prevalent in water treatment plants, where it is used to control pumps, valves, and filtration systems. The ability to represent discrete control operations aligns with the on/off nature of many water treatment processes.

Elevator Control Systems:

Elevator control systems leverage Ladder Logic to coordinate the operation of motors, doors, and safety features. The sequential nature of Ladder Logic is well-suited for managing the step-by-step process of elevator operation.

## Programming Best Practices:

Use of Descriptive Labels:

Clearly label contacts, coils, and other elements with descriptive names to enhance program readability and understanding.

Structured Organization:

Organize the ladder diagram in a structured manner, with input conditions at the beginning and output actions at the end of each rung. This facilitates easy navigation and maintenance.

Documentation:

Provide comprehensive documentation for the Ladder Logic program, including comments and annotations. This documentation aids in troubleshooting and future modifications.

Testing and Simulation:

Prior to deploying a Ladder Logic program in a live environment, thoroughly test and simulate its behavior. Simulation allows for the identification and correction of errors without the risk of disrupting actual processes.

## Example of Ladder Logic Program:

Ladder Logic program for a start-stop motor control scenario.

–[ Start Button ]—-[ Motor Coil )–[ Stop Button ]–

In this example, we’ll use two push buttons: one for starting the motor (Start button) and another for stopping the motor (Stop button). The motor will be represented by a coil.

Start Button (Normally Open Contact):

The leftmost part of the ladder diagram represents the Start button. It is a normally open contact, symbolized by “–[ ]–“. This means the contact is closed (or active) only when the Start button is pressed.

Motor Coil:

In the middle, there is the Motor Coil, represented by “–( )–“. This coil represents the motor and will be energized when the Start button is pressed.

## Stop Button (Normally Closed Contact):

On the right side, there is the Stop button represented by “–[ ]–“. However, notice the orientation of the brackets; it is a normally closed contact. This means the contact is normally closed and becomes open (inactive) when the Stop button is pressed.

Execution Flow:

When the Start button is pressed, the normally open contact associated with it closes, allowing current to flow to the Motor Coil. The Motor Coil energizes, and the motor starts running.

Simultaneously, the normally closed contact associated with the Stop button opens, breaking the circuit. Even if the Stop button is pressed, it won’t affect the operation because the normally closed contact is already open.

Stop Operation:

To stop the motor, the Stop button must be pressed. This action opens the normally closed contact associated with the Stop button, breaking the circuit to the Motor Coil. The Motor Coil de-energizes, and the motor stops.

This simple Ladder Logic program demonstrates the basic principles of control in industrial automation. It uses the graphical representation to show the sequential flow of logic, making it easy to understand and troubleshoot. The start-stop motor control scenario is a fundamental example, but in real-world applications, Ladder Logic can be extended to control more complex processes and machinery by adding additional rungs and incorporating timers, counters, and other logical operations.

## Future Trends and Adaptations:

As industries evolve towards greater connectivity and automation, the role of ladder Logic continues to adapt. Integration with higher-level programming languages , the incorporation of advanced communication protocols , and compatibility with Industry 4.0 principles are becoming increasingly relevant. Ladder Logic remains a foundational element, often used in conjunction with other programming languages to create comprehensive control systems that meet the demands of modern industrial processes.

Please refer to this link for Ladder Logic MCQs .

From controlling manufacturing processes to orchestrating traffic signals, Ladder Logic continues to play a pivotal role in shaping the efficiency and reliability of industrial automation.

- Data Structures
- Linked List
- Binary Tree
- Binary Search Tree
- Segment Tree
- Disjoint Set Union
- Fenwick Tree
- Red-Black Tree
- Advanced Data Structures
- Graph Data Structure And Algorithms
- Introduction to Graphs - Data Structure and Algorithm Tutorials
- Graph and its representations
- Types of Graphs with Examples
- Basic Properties of a Graph

## Applications, Advantages and Disadvantages of Graph

- Transpose graph
- Difference Between Graph and Tree

## BFS and DFS on Graph

- Breadth First Search or BFS for a Graph
- Depth First Search or DFS for a Graph
- Applications, Advantages and Disadvantages of Depth First Search (DFS)
- Applications, Advantages and Disadvantages of Breadth First Search (BFS)
- Iterative Depth First Traversal of Graph
- BFS for Disconnected Graph
- Transitive Closure of a Graph using DFS
- Difference between BFS and DFS

## Cycle in a Graph

- Detect Cycle in a Directed Graph
- Detect cycle in an undirected graph
- Detect Cycle in a directed graph using colors
- Detect a negative cycle in a Graph | (Bellman Ford)
- Cycles of length n in an undirected and connected graph
- Detecting negative cycle using Floyd Warshall
- Clone a Directed Acyclic Graph

## Shortest Paths in Graph

- How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm
- Bellman–Ford Algorithm
- Floyd Warshall Algorithm
- Johnson's algorithm for All-pairs shortest paths
- Shortest Path in Directed Acyclic Graph
- Multistage Graph (Shortest Path)
- Shortest path in an unweighted graph
- Karp's minimum mean (or average) weight cycle algorithm
- 0-1 BFS (Shortest Path in a Binary Weight Graph)
- Find minimum weight cycle in an undirected graph

## Minimum Spanning Tree in Graph

- Kruskal’s Minimum Spanning Tree (MST) Algorithm
- Difference between Prim's and Kruskal's algorithm for MST
- Applications of Minimum Spanning Tree
- Total number of Spanning Trees in a Graph
- Minimum Product Spanning Tree
- Reverse Delete Algorithm for Minimum Spanning Tree

## Topological Sorting in Graph

- Topological Sorting
- All Topological Sorts of a Directed Acyclic Graph
- Kahn's algorithm for Topological Sorting
- Maximum edges that can be added to DAG so that it remains DAG
- Longest Path in a Directed Acyclic Graph
- Topological Sort of a graph using departure time of vertex

## Connectivity of Graph

- Articulation Points (or Cut Vertices) in a Graph
- Biconnected Components
- Bridges in a graph
- Eulerian path and circuit for undirected graph
- Fleury's Algorithm for printing Eulerian Path or Circuit
- Strongly Connected Components
- Count all possible walks from a source to a destination with exactly k edges
- Euler Circuit in a Directed Graph
- Word Ladder (Length of shortest chain to reach a target word)
- Find if an array of strings can be chained to form a circle | Set 1
- Tarjan's Algorithm to find Strongly Connected Components
- Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
- Dynamic Connectivity | Set 1 (Incremental)

## Maximum flow in a Graph

- Max Flow Problem Introduction
- Ford-Fulkerson Algorithm for Maximum Flow Problem
- Find maximum number of edge disjoint paths between two vertices
- Find minimum s-t cut in a flow network
- Maximum Bipartite Matching
- Channel Assignment Problem
- Introduction to Push Relabel Algorithm
- Introduction and implementation of Karger's algorithm for Minimum Cut
- Dinic's algorithm for Maximum Flow

## Some must do problems on Graph

- Find size of the largest region in Boolean Matrix
- Count number of trees in a forest
- A Peterson Graph Problem
- Clone an Undirected Graph
- Introduction to Graph Coloring
- Traveling Salesman Problem (TSP) Implementation
- Introduction and Approximate Solution for Vertex Cover Problem
- Erdos Renyl Model (for generating Random Graphs)
- Chinese Postman or Route Inspection | Set 1 (introduction)
- Hierholzer's Algorithm for directed graph
- Boggle (Find all possible words in a board of characters) | Set 1
- Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction)
- Construct a graph from given degrees of all vertices
- Determine whether a universal sink exists in a directed graph
- Number of sink nodes in a graph
- Two Clique Problem (Check if Graph can be divided in two Cliques)

Graph is a non-linear data structure that contains nodes (vertices) and edges. A graph is a collection of set of vertices and edges (formed by connecting two vertices). A graph is defined as G = {V, E} where V is the set of vertices and E is the set of edges.

Graphs can be used to model a wide variety of real-world problems, including social networks, transportation networks, and communication networks. They can be represented in various ways, such as by a set of vertices and a set of edges, or by a matrix or an adjacency list. The two most common types of graphs are directed and undirected graphs.

Terminologies of Graphs:

.An edge is one of the two primary units used to form graphs. Each edge has two ends, which are vertices to which it is attached.

.If two vertices are endpoints of the same edge, they are adjacent.

.A vertex’s outgoing edges are directed edges that point to the origin.

.A vertex’s incoming edges are directed edges that point to the vertex’s destination.

.The total number of edges occurring to a vertex in a graph is its degree.

.A vertex with an in-degree of zero is referred to as a source vertex, while one with an out-degree of zero is known as sink vertex.

.A path is a set of alternating vertices and edges, with each vertex connected by an edge.

.The path that starts and finishes at the same vertex is known as a cycle.

.A path with unique vertices is called a simple path.

.A spanning subgraph that is also a tree is known as a spanning tree.

.A connected component is the unconnected graph’s most connected subgraph.

.A bridge, which is an edge of removal, would sever the graph.

.Forest is a graph without a cycle.

Graph Representation :

Graph can be represented in the following ways:

- Set Representation: Set representation of a graph involves two sets: Set of vertices V = {V 1 , V 2 , V 3 , V 4 } and set of edges E = {{V 1 , V 2 }, {V 2 , V 3 }, {V 3 , V 4 }, {V 4 , V 1 }} . This representation is efficient for memory but does not allow parallel edges.
- Adjacency Matrix: This matrix includes information about the adjacent nodes. Here, a ij = 1 if there is an edge from V i to V j otherwise 0 . It is a matrix of order V×V .
- Incidence Matrix: This matrix includes information about the incidence of edges on the nodes. Here, a ij = 1 if the j th edge E j is incident on i th vertex V i otherwise 0 . It is a matrix of order V×E.
- Path Matrix: This matrix includes information about the simple path between two vertices. Here, P ij = 1 if there is a path from V i to V j otherwise 0 . It is also called as reachability matrix of graph G .
- Linked Representation: This representation gives the information about the nodes to which a specific node is connected i.e. adjacency lists. This representation gives the adjacency lists of the vertices with the help of array and linked lists. In the adjacency lists, the vertices which are connected with the specific vertex are arranged in the form of lists which is connected to that vertex.

Real-Time Applications of Graph:

- Social media analysis : Social media platforms generate vast amounts of data in real-time, which can be analyzed using graphs to identify trends, sentiment, and key influencers. This can be useful for marketing, customer service, and reputation management.
- Network monitoring: Graphs can be used to monitor network traffic in real-time, allowing network administrators to identify potential bottlenecks, security threats, and other issues. This is critical for ensuring the smooth operation of complex networks.
- Financial trading: Graphs can be used to analyze real-time financial data, such as stock prices and market trends, to identify patterns and make trading decisions. This is particularly important for high-frequency trading, where even small delays can have a significant impact on profits.
- Internet of Things (IoT) management: IoT devices generate vast amounts of data in real-time, which can be analyzed using graphs to identify patterns, optimize performance, and detect anomalies. This is important for managing large-scale IoT deployments.
- Autonomous vehicles: Graphs can be used to model the real-time environment around autonomous vehicles, allowing them to navigate safely and efficiently. This requires real-time data from sensors and other sources, which can be processed using graph algorithms.
- Disease surveillance : Graphs can be used to model the spread of infectious diseases in real-time, allowing health officials to identify outbreaks and implement effective containment strategies. This is particularly important during pandemics or other public health emergencies.
- The best example of graphs in the real world is Facebook. Each person on Facebook is a node and is connected through edges. Thus, A is a friend of B. B is a friend of C, and so on.

Advantages of Graph:

- Representing complex data: Graphs are effective tools for representing complex data, especially when the relationships between the data points are not straightforward. They can help to uncover patterns, trends, and insights that may be difficult to see using other methods.
- Efficient data processing: Graphs can be processed efficiently using graph algorithms, which are specifically designed to work with graph data structures. This makes it possible to perform complex operations on large datasets quickly and effectively.
- Network analysis: Graphs are commonly used in network analysis to study relationships between individuals or organizations, as well as to identify important nodes and edges in a network. This is useful in a variety of fields, including social sciences, business, and marketing.
- Pathfinding: Graphs can be used to find the shortest path between two points, which is a common problem in computer science, logistics, and transportation planning.
- Visualization : Graphs are highly visual, making it easy to communicate complex data and relationships in a clear and concise way. This makes them useful for presentations, reports, and data analysis.
- Machine learning : Graphs can be used in machine learning to model complex relationships between variables, such as in recommendation systems or fraud detection.
- Graphs are used in computer science to depict the flow of computation.
- Users on Facebook are referred to as vertices, and if they are friends, there is an edge connecting them. The Friend Suggestion system on Facebook is based on graph theory.
- You come across the Resources Allocation Graph in the Operating System, where each process and resource are regarded vertically. Edges are drawn from resources to assigned functions or from the requesting process to the desired resources. A stalemate will develop if this results in the establishment of a cycle.
- Web pages are referred to as vertices on the World Wide Web. Suppose there is a link from page A to page B that can represent an edge. this application is an illustration of a directed graph.
- Graph transformation systems manipulate graphs in memory using rules, Graph databases store and query graph-structured data in a transaction-safe, perment manner.

Disadvantages of Graph:

- Limited representation: Graphs can only represent relationships between objects, and not their properties or attributes. This means that in order to fully understand the data, it may be necessary to supplement the graph with additional information.
- Difficulty in interpretation: Graphs can be difficult to interpret, especially if they are large or complex. This can make it challenging to extract meaningful insights from the data, and may require advanced analytical techniques or domain expertise.
- Scalability issue s: As the number of nodes and edges in a graph increases, the processing time and memory required to analyze it also increases. This can make it difficult to work with large or complex graphs.
- Data quality issues : Graphs are only as good as the data they are based on, and if the data is incomplete, inconsistent, or inaccurate, the graph may not accurately reflect the relationships between objects.
- Lack of standardization : There are many different types of graphs, and each has its own strengths and weaknesses. This can make it difficult to compare graphs from different sources, or to choose the best type of graph for a given analysis.
- Privacy concerns : Graphs can reveal sensitive information about individuals or organizations, which can raise privacy concerns, especially in social network analysis or marketing.

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## Computer Science > Machine Learning

Title: subgraph2vec: a random walk-based algorithm for embedding knowledge graphs.

Abstract: Graph is an important data representation which occurs naturally in the real world applications \cite{goyal2018graph}. Therefore, analyzing graphs provides users with better insights in different areas such as anomaly detection \cite{ma2021comprehensive}, decision making \cite{fan2023graph}, clustering \cite{tsitsulin2023graph}, classification \cite{wang2021mixup} and etc. However, most of these methods require high levels of computational time and space. We can use other ways like embedding to reduce these costs. Knowledge graph (KG) embedding is a technique that aims to achieve the vector representation of a KG. It represents entities and relations of a KG in a low-dimensional space while maintaining the semantic meanings of them. There are different methods for embedding graphs including random walk-based methods such as node2vec, metapath2vec and regpattern2vec. However, most of these methods bias the walks based on a rigid pattern usually hard-coded in the algorithm. In this work, we introduce \textit{subgraph2vec} for embedding KGs where walks are run inside a user-defined subgraph. We use this embedding for link prediction and prove our method has better performance in most cases in comparison with the previous ones.

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## Node Classification in Weighted Complex Networks Using Neighborhood Feature Similarity

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## Preprint

- Preprint egusphere-2024-1303

## Graphical representation of global water models

Abstract. Numerical models are simplified representations of the real world at a finite level of complexity. Global water models are used to simulate the global water cycle and their outputs contribute to the evaluation of important natural and societal issues, including water availability, flood risk and ecological functioning. Whilst global water modelling is an area of science that has developed over several decades, and individual model-specific descriptions exist for some models, there has to date been no attempt to visualize the ways that several models work, using a standardized visualisation framework. Here, we address this gap by presenting a set of visualizations of several global water models participating in the Inter-Sectoral Impact Model Intercomparison Project phase 2b (ISIMIP2b). The diagrams were co-produced between a graphics designer and 16 modelling teams, based on extensive discussions and pragmatic decision-making that balanced the need for accuracy and detail against the need for effective visualization. The model diagrams are based on a standardized "ideal" global water model that represents what is theoretically possible to represent in the current generation of state-of-the-art global water models participating in ISIMIP2b. Model-specific diagrams are then copies of the "ideal" model, with individual processes either included or greyed out. As well as serving an educational purpose, we envisage that the diagrams will help researchers in and outside of the global water model community to select the suitable model(s) for specific applications, stimulate a community learning process, and identify missing components to help direct future model developments.

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## Model code and software

Prototype for automatic model diagram generation Hannes Müller Schmied https://github.com/hmschmie/automodeldiagram

## Viewed (geographical distribution)

Hannes müller schmied, simon newland gosling, marlo garnsworthy, laura müller, camelia-eliza telteu, atiq kainan ahmed, lauren seaby andersen, julien boulange, peter burek, jinfeng chang, manolis grillakis, luca guillaumot, naota hanasaki, aristeidis koutroulis, rohini kumar, guoyong leng, xingcai liu, vimal mishra, yadu pokhrel, oldrich rakovec, luis samaniego, yusuke satoh, harsh lovekumar shah, mikhail smilovic, tobias stacke, edwin sutanudjaja, athanasios tsilimigkras, yoshihide wada, niko wanders, tokuta yokohata.

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