🚀 Graph-Theory-Visualizer

This project is a Graph Theory Visualizer created using the Manim animation library. It is designed to visually explain basic concepts of graph theory, focusing on graph counting, non-isomorphic graphs, and isomorphism. This project was developed as part of a homework assignment for a Graph Theory course at Akdeniz University.

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🌐 Project Overview

This project includes:

• Visualizing the concept of simple graphs and counting them.
• Illustrating the concept of isomorphic graphs.
• Animating graph structures to enhance understanding.

The project currently focuses on:

• Counting simple graphs for n=3 and n=4.
• Identifying and explaining isomorphic graphs.

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🚀 How to Run

✅ Prerequisites

• Make sure you have Manim Community (v0.19) installed:

  pip install manim ```

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• Ensure that LaTeX (MikTeX) is installed for mathematical formulas.

✅ Running the Animation

1. Clone the repository:

   git clone https://github.com/Akdeniz-CSE-Students/Graph-Theory-Visualizer.git
   cd Graph-Theory-Visualizer

2. Run the Manim animation:

   manim -pql graph_counting_n4_test.py CountingGraphsComplete

3. Your animation will be created in the media/videos directory.

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📚 Understanding the Animation

🔹 Part 1: Introduction

• The animation begins with an introduction to the concept of graph counting.

• It introduces the mathematical formula for calculating the total number of edges in a graph:

  $$ B(n, 2) = \frac{n(n - 1)}{2} $$

🔹 Part 2: Graphs for n=3

• It displays all 8 possible simple graphs for n=3.
• Isomorphic graphs are faded out for clarity.
• An isomorphism example is shown with a visual explanation.

🔹 Part 3: Graphs for n=4

• It presents the 11 unique non-isomorphic graphs for n=4 among the 64 possible combinations.
• This section is designed to clearly show how isomorphism reduces the total number of unique graphs.

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📌 Why This Project?

This project was created as part of a homework assignment for Graph Theory. The goal is to help students understand:

• How simple graphs can be counted.
• How isomorphic graphs are identified.
• The concept of non-isomorphic graphs for different values of n.

✨ Assigned Slide for Student ID: 20220808005

• This project is the visual representation of Slide 23 in the assigned homework slides.

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🌐 Contributing

If you are a student working on a similar homework, you can:

• Fork this repository.
• Create your own graph visualizations.
• Make a pull request with your contribution.

✅ Recommended Contribution:

• Create a new file for your slide (e.g., example.py).
• Follow the structure of the existing code.
• Add a brief description of your animation to the README.

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👤 Author

• Yahya Efe Kuruçay - Student ID: 20220808005
• 📌 My Website
• 📌 My GitHub Profile
• 📌 Akdeniz CSE Students GitHub

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📌 License

This project is open-source and available under the MIT License. Feel free to use and modify it for educational purposes. 😊