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Community Detection in Large-Scale Complex Networks via Structural Entropy Game

Yantuan Xian, Pu Li, Hao Peng, Zhengtao Yu, Yan Xiang, Philip S. Yu

TL;DR

This paper tackles the challenge of detecting communities in large-scale networks by introducing CoDeSEG, a fast heuristic that minimizes the two-dimensional structural entropy (2DSE) within a community formation game. The method defines node-level strategies (Stay, Leave, Transfer) and a structural-entropy-based overlap heuristic, achieving near-linear time for non-overlapping and overlapping detection, respectively. Empirical results on real-world networks show state-of-the-art performance in overlapping metrics (ONMI and F1) and strong non-overlapping results, with substantial runtime improvements (average ~45x faster than the fastest baseline) and rapid convergence. The approach is flexible across graph types (unweighted/weighted, directed/undirected) and highly parallelizable, making it practical for networks with millions of nodes; code is publicly available to facilitate adoption and further research.

Abstract

Community detection is a critical task in graph theory, social network analysis, and bioinformatics, where communities are defined as clusters of densely interconnected nodes. However, detecting communities in large-scale networks with millions of nodes and billions of edges remains challenging due to the inefficiency and unreliability of existing methods. Moreover, many current approaches are limited to specific graph types, such as unweighted or undirected graphs, reducing their broader applicability. To address these issues, we propose a novel heuristic community detection algorithm, termed CoDeSEG, which identifies communities by minimizing the two-dimensional (2D) structural entropy of the network within a potential game framework. In the game, nodes decide to stay in current community or move to another based on a strategy that maximizes the 2D structural entropy utility function. Additionally, we introduce a structural entropy-based node overlapping heuristic for detecting overlapping communities, with a near-linear time complexity.Experimental results on real-world networks demonstrate that CoDeSEG is the fastest method available and achieves state-of-the-art performance in overlapping normalized mutual information (ONMI) and F1 score.

Community Detection in Large-Scale Complex Networks via Structural Entropy Game

TL;DR

This paper tackles the challenge of detecting communities in large-scale networks by introducing CoDeSEG, a fast heuristic that minimizes the two-dimensional structural entropy (2DSE) within a community formation game. The method defines node-level strategies (Stay, Leave, Transfer) and a structural-entropy-based overlap heuristic, achieving near-linear time for non-overlapping and overlapping detection, respectively. Empirical results on real-world networks show state-of-the-art performance in overlapping metrics (ONMI and F1) and strong non-overlapping results, with substantial runtime improvements (average ~45x faster than the fastest baseline) and rapid convergence. The approach is flexible across graph types (unweighted/weighted, directed/undirected) and highly parallelizable, making it practical for networks with millions of nodes; code is publicly available to facilitate adoption and further research.

Abstract

Community detection is a critical task in graph theory, social network analysis, and bioinformatics, where communities are defined as clusters of densely interconnected nodes. However, detecting communities in large-scale networks with millions of nodes and billions of edges remains challenging due to the inefficiency and unreliability of existing methods. Moreover, many current approaches are limited to specific graph types, such as unweighted or undirected graphs, reducing their broader applicability. To address these issues, we propose a novel heuristic community detection algorithm, termed CoDeSEG, which identifies communities by minimizing the two-dimensional (2D) structural entropy of the network within a potential game framework. In the game, nodes decide to stay in current community or move to another based on a strategy that maximizes the 2D structural entropy utility function. Additionally, we introduce a structural entropy-based node overlapping heuristic for detecting overlapping communities, with a near-linear time complexity.Experimental results on real-world networks demonstrate that CoDeSEG is the fastest method available and achieves state-of-the-art performance in overlapping normalized mutual information (ONMI) and F1 score.
Paper Structure (31 sections, 22 equations, 7 figures, 5 tables, 2 algorithms)

This paper contains 31 sections, 22 equations, 7 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Community Detection
  4. Community Formation Game
  5. Structural Entropy
  6. Methodology
  7. Structural Entropy based Heuristic Function
  8. Efficient computation of $\Delta_{\text{L}}(x, \mathcal{C}_k)$
  9. Community Detection Algorithm
  10. Non-overlapping Community Detection
  11. Overlapping Community Detection
  12. Time Complexity
  13. Parallelism Implementation
  14. Experiments
  15. Experimental Setups
  16. ...and 16 more sections

Figures (7)

  • Figure 1: Illustration of non-overlapping and overlapping community structures in a network.
  • Figure 2: Overview of the proposed CoDeSEG algorithm.
  • Figure 3: Convergence of CoDeSEG on Amazon and DBLP.
  • Figure 4: F1 score of each iteration on Amazon and DBLP.
  • Figure 5: F1 scores and runtime on LiveJournal and Orkut with different threads.
  • ...and 2 more figures

Theorems & Definitions (3)

  • definition 1: Strategy Profile
  • definition 2: Utility Function
  • definition 3: Potential Game