Community Detection in Networks: A Rough Sets and Consensus Clustering Approach

TL;DR

RC-CCD introduces a Rough Set Theory–based consensus framework for community detection that aggregates multiple partitions to produce a robust network covering with clearly delineated cores and boundary regions. By constructing granules through a $\beta$-thresholded similarity graph and refining them with rough $k$-means, RC-CCD achieves high accuracy and stability on LFR synthetic networks, outperforming baselines in challenging, complex topologies. The method demonstrates strong core accuracy (>$90\%$) and effective overlap detection, with performance tunable via $\gamma$ and $\beta$ to adapt to network size and complexity. This approach provides a practical, flexible tool for accurate community detection in social and biological networks, with clear avenues for extending to real-world and dynamic systems.

Abstract

The objective of this paper is to propose a framework, called Rough Clustering-based Consensus Community Detection (RC-CCD), to effectively address the challenge of identifying community structures in complex networks from a set of different community partitions. The method uses a consensus approach based on Rough Set Theory (RST) to manage uncertainty and improve the reliability of community detection. The RC-CCD framework is tested on synthetic benchmark networks generated by the Lancichinetti-Fortunato-Radicchi (LFR) method, which simulate varying network scales, node degrees, and community sizes. Key findings demonstrate that RC-CCD outperforms established algorithms like Louvain, Greedy, and LPA in terms of normalized mutual information, showing superior accuracy and adaptability, particularly in networks with higher complexity, both in terms of size and dispersion. These results have significant implications for enhancing community detection in fields such as social and biological network analysis.

Figures (8)

• Figure 1: Summary of the RC-CCD process: (1) Compute the similarity $S_{_{\mathbb{NP}}}$ between vertex pairs based on shared communities across partitions $\mathbb{NP}$; (2) Construct the $\beta$-similarity graph and identify its connected components; (3) Identify induced subgraphs in the original graph as sets of inseparable nodes; (4) Select the largest $k$ granules as community prototypes, and assign remaining granules to lower or upper approximations using the similarity function $CS_{_{G_{rj}}}$ and $\gamma$ threshold; (5) Output communities with core and boundary members.
• Figure 2: Comparison of the base algorithms and RC-CCD on $LFR$ benchmark.
• Figure 3: Comparison of Participation Coefficient values for overlapping nodes identified by RC-CCD and ground-truth communities overlapping nodes on the $LFR$ benchmark.
• Figure 4: Comparison of base algorithms and RC-CCD (with varying $\gamma$ settings) outcomes on the $LFR$ benchmark.
• Figure 5: Small Network Configuration. Summary of Results for Different $\mu$ Values

Theorems & Definitions (4)

• Definition 1: Thresholded similarity graph
• Definition 2: Subgraph
• Definition 3: Induced Subgraph
• Definition 4: $\beta$-Connected Component