🕸️ Graph Theory Visualizer

A Svelte 5-based interactive tool for visualizing and analyzing directed graphs with support for graph operations, traversal, and isomorphism detection. 📊

🚀 Features

• ✅ Directed Graph Visualization - All graphs are directed by default
• 🔍 Auto-detection - Automatically identifies multi-graphs and simple graphs
• 🧭 Graph Traversal - Traverse existing graphs (subgraphs can be created but not traversed)
• 🔄 Isomorphism Detection - Check if Graph A and Graph B are isomorphic
• ⚡ Reactive Inputs - Real-time state updates as you modify graph data

🛠️ Tech Stack

• Framework: Svelte 5 with TypeScript v4
• Libraries:
  • 👁️ vis-network - Graph network visualization
  • 📝 parser - Input conversion and parsing
  • ⚙️ operations - Graph transformation tasks
  • 🔬 analyzer - Graph theoretical analysis

🏁 Getting Started

# Clone the repository
git clone <repo>

# Install dependencies and run
pnpm run dev

📝 Input Format

Adjacency List

Represent graphs using adjacency lists where the index corresponds to the node ID:

// Simple graph
[[2,3], [], [0,3], [0,2]]

Traversal Path

Specify a path through the graph:

[0,2,0]

💡 Examples

Example 1: Complete Graph K₄

// Each node connected to all others
[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]

Example 2: Multi-graph with Traversal 🔀

// Graph with multiple edges
[[2,3,3], [], [0,3], [0,0,2,3,3]]

// Traversal paths
[0,1,3,1]
[0,2,0]

Example 3: Graph Operations 🧮

Graph A:

[[1,2], [0,2], [0,1,3], [2]]

Graph B:

[[1,3], [0,2], [1,3], [0,2]]

Union ∪ (nodes connected if edge exists in either graph):

[[1,2,3], [0,2], [0,1,3], [0,2,3]]

Intersection ∩ (nodes connected only if edge exists in both graphs):

[[1], [0,2], [1,3], [2]]

Cartesian Product × :

0: [1, 3, 4, 8]
1: [0, 2, 5, 9]
2: [1, 3, 6, 10]
3: [0, 2, 7, 11]
4: [0, 5, 7, 8]
5: [1, 4, 6, 9]
6: [2, 5, 7, 10]
7: [3, 4, 6, 11]
8: [0, 4, 9, 11, 12]
9: [1, 5, 8, 10, 13]
10: [2, 6, 9, 11, 14]
11: [3, 7, 8, 10, 15]
12: [8, 13, 15]
13: [9, 12, 14]
14: [10, 13, 15]
15: [11, 12, 14]

⚠️ Known Issues

Current Limitations:

1. 🐌 Performance - Slow due to unoptimized use of Svelte 5's $effect rune
2. 🍝 Input Validation - Complex validation logic needs refactoring
3. 📱 Responsive Layout - Container breaks on smaller screens
4. 🚫 Multi-graph Support - Graph operations currently don't work on multi-graphs

🤝 Contributing

Contributions are welcome! Feel free to submit issues and pull requests. 💪

📄 License

[Add your license here]