A Constrained Louvain Algorithm with Novel Modularity for Enhanced Community Detection in Complex Networks

Abstract

Background: Community detection in complex networks is a crucial task with applications spanning social networks, biology, and information retrieval. However, conventional algorithms, particularly modularity-based methods, often struggle with the intricate community structures found in extensive networks due to the "resolution limit" problem.

Aim: This research aims to advance community detection by introducing the constrained Louvain algorithm with 𝐹2 modularity. The 𝐹2 modularity function overcomes traditional modularity's limitations by considering both the quantity and distribution of edges within communities. It effectively mitigates the resolution limit problem, enabling the detection of both large and small communities.

Methodology: The novel constrained Louvain algorithm with 𝐹2 modularity is presented. It combines the computational efficiency of the Louvain algorithm with 𝐹2 modularity's ability to provide accurate and fine-grained community assessments. The algorithm proceeds in iterative steps, optimizing community assignments by considering intra-community degree distributions.

Results and Discussion: Experimental evaluations demonstrate the superiority of the proposed algorithm. It consistently outperforms both the classical Louvain algorithm and Newman's fast algorithm across synthetic benchmark and real-world network datasets. The constrained Louvain algorithm with 𝐹2 modularity excels in optimizing Normalized Mutual Information (NMI) and Modularity (Q), indicating its effectiveness in detecting communities accurately.

Conclusion: This study introduces an innovative approach to community detection in complex networks. The constrained Louvain algorithm with 𝐹2 modularity effectively overcomes the limitations of traditional modularity, particularly the resolution limit problem. It facilitates accurate and fine-grained community detection, making it a valuable tool for analyzing extensive networks across various domains. This research contributes to the ongoing efforts to enhance our understanding of network structures and dynamics by providing a robust community detection methodology.