Effective Resistance-Based Graph Sparsification and Community Detection

2026-06-25

AI Summary

This study addresses the limitations of existing community detection methods in complex networks, particularly their insufficient accuracy and computational inefficiency. To overcome these challenges, the authors propose a novel and efficient approach that integrates effective resistance-based node similarity with graph sparsification. Specifically, they introduce effective resistance as a similarity measure for the first time in community detection, construct a weighted graph, and then generate a structure-preserving sparse graph by combining a minimum spanning tree with threshold-based sparsification. The Clauset–Newman–Moore modularity maximization algorithm is subsequently applied to this sparse graph. Experimental results on both synthetic and real-world networks demonstrate that the proposed method consistently outperforms state-of-the-art algorithms, achieving higher accuracy in identifying community structures while significantly improving computational efficiency.

Abstract

Community detection is a key task in network analysis, providing insight into the structural organization of complex systems. Effective resistance, a graph-theoretic metric derived from electrical network theory, has emerged as a powerful tool for evaluating connectivity and influence within networks. This paper proposes an effective resistance-based community detection algorithm that calculates the similarity between nodes using effective resistance values and produces a weighted graph. The sparse graph used in the algorithm is generated after computing the minimum spanning tree (MST) of the weighted graph and adopting a threshold sparsification strategy on non-MST edges. A maximum modularity approach is adopted using the Clauset-Newman-Moore algorithm on the resultant sparse graph. This algorithm is evaluated for both synthetic and real-world networks, demonstrating its effectiveness compared to popular existing methods. The result shows that the effective resistance-based approach accurately captures the structures of the community while maintaining computational efficiency.

Problem

• Community Detection
• Graph Sparsification
• Effective Resistance
• Network Analysis
• Modularity

Innovation

• effective resistance
• graph sparsification
• community detection
• minimum spanning tree
• modularity maximization