📚 Community Detection Algorithms

Now it's a library! Check out the implementation also on Pypi link

pip install SelfImplemented-Community-Detection-Algorithms-Improved==0.1.0

📝 Overview

This library implements community detection algorithms with a focus on:

• Performance Optimization
• Flexibility
• Traceability
• Modularity

Compared to NetworkX's native algorithms, our custom implementation delivers measurable performance gains, customizable strategies, and transparent debugging logs.

Girvan-Newman Algorithm for Community Detection

• Purpose: Identify communities by removing edges with the highest betweenness centrality.
• Customizable Methods:
  • Betweenness Calculation: bfs | dijkstra
  • Component Detection: dfs_recursive | dfs_iterative

⚠️ Custom Method: BFS | Component Method: DFS Recursive

Metric	Custom	NetworkX	Difference	% Improvement
Execution Time	0.0380s	0.0265s	0.0115s	-30.25%

✅ Communities Match: Yes

⚠️ Custom Method: BFS | Component Method: DFS Iterative

Metric	Custom	NetworkX	Difference	% Improvement
Execution Time	0.0281s	0.0265s	0.0016s	-6.04%

✅ Communities Match: Yes

⚠️ Custom Method: Dijkstra | Component Method: DFS Recursive

Metric	Custom	NetworkX	Difference	% Improvement
Execution Time	0.0176s	0.0274s	0.0098s	35.77%

✅ Communities Match: Yes

⚠️ Custom Method: Dijkstra | Component Method: DFS Iterative

Metric	Custom	NetworkX	Difference	% Improvement
Execution Time	0.0164s	0.0264s	0.0100s	37.88%

✅ Communities Match: Yes

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Spectral Clustering

• Purpose: Partition the graph using the eigenvalues and eigenvectors of its Laplacian matrix.

Key Improvements:

• Faster convergence with optimized eigenvalue sorting.
• Transparent iteration logs for eigenvector refinement.

⏱️ Performance Comparison:

Metric	Custom Spectral	Pre-Implemented	Difference	% Improvement
Execution Time	0.0179s	0.2326s	0.2147s	92.28%

✅ Communities Match: Yes

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Louvain Method

• Use of math-based methods to improve running time. Source of the study linked here

⏱️ Performance Comparison:

Metric	Custom Louvain	Pre-Implemented	Difference	% Improvement
Execution Time	0.0000000000s	0.0039553642s	0.0039s	4000000%
Modularity	0.4187	0.4449	-0.0262	-5.89%

❌ Communities Do NOT Match:

🔑 Node Importance (Lambiotte Coefficient):

Node	Coefficient
0	0.9048
3	1.0

🔑 Community Strength (Clauset's Parameter):

Community	Strength
0	0.9
1	0.9091

The Custom method aligns well with the pre-implemented approach for major communities, though it sometimes splits larger communities into smaller subsets (This is probably because Nx cuts the creation of new communities if doing it adds gains under a certain threshold). Its strength btw is its computational efficiency: it runs a lot faster than the pre-implemented function, but the gain in computational resources can be useful in the computational-expensive tasks, with the right trade-off between efficiency and quality of results

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🛠️ How to Use the Methods

1️⃣ Girvan-Newman Algorithm

The Girvan-Newman Algorithm identifies communities by iteratively removing edges with the highest betweenness centrality.

Configuration Options:

• betweenness_method: Choose between "bfs" (default) or "dijkstra" for betweenness calculation.
• component_method: Choose between "dfs_recursive" (default) or "dfs_iterative" for connected component detection.

Example Usage:

betweenness_method = "bfs"  # Options: "bfs", "dijkstra"
component_method = "dfs_recursive"  # Options: "dfs_recursive", "dfs_iterative"

# Run Girvan-Newman Algorithm
communities, removed_edges = custom_girvan_newman(G, betweenness_method, component_method)
# Visualize Results
visualize_communities(G, communities, removed_edges)

2️⃣ Spectral Clustering

Spectral Clustering uses the eigenvalues and eigenvectors of a graph's Laplacian matrix to detect communities.

Configuration Options:

• k: Number of clusters to detect.

Example Usage:

edges = list(nx_G.edges())  # Extract unweighted edges
G = Graph(edges) # Convert to custom graph object
print("\n--- Spectral Clustering ---")
spectral_communities = spectral_clustering(G, k=2)
print("Spectral Communities:", spectral_communities)

3️⃣ Louvain Method

The Louvain Method detects communities by maximizing modularity in hierarchical clustering.

Configuration Options:

• max_iter: Number of iterations for optimizing modularity. Example Usage:

import networkx as nx
adj_matrix = nx.to_numpy_array(nx_G)
communities = louvain_cluster(adj_matrix, max_iter=10)
print("\nDetected Communities:", communities)

For documentation, usage examples, and contribution guidelines, refer to the repository. 🚀