Transcending modularity: A memetic algorithm combining triangle motif and edge information for community detection

Abstract

The research towards community detection plays a crucial role in revealing the topological structure and functional characteristics of complex networks. Nowadays, modularity and its variants are the most popular community quality evaluation metric applied in the detection of community structures. However, these modularity-based methods rarely consider higher-order structural information such as motifs in a network, which may lead to an incomplete and inaccurate understanding of the network. While some motif-based methods have been proposed, they suffer from resolution limitations and completely ignore lower-order structures. To bridge this gap and address community detection problem from a more hybrid view focusing on both lower-order and higher-order structures, this paper first proposes an adaptive hybrid-order modularity optimization function termed as TE-Modularity, which harmonizes triangle motif and edge information. It transcends traditional modularity by considering both lower-order and higher-order structures and can be applicable to all types of networks. In addition, we design a memetic algorithm called TE-MA, that uses TE-Modularity as the objective function to solve the community detection problem. A novel mutation operator based on triangle motifs is proposed, which can effectively accelerate the convergence of the proposed algorithm. Furthermore, we develop a new multipoint local search strategy, striking a good balance between the efficiency and quality of the algorithm. Through experiments conducted on different optimizers and comparisons with several state-of-the-art community detection methods, our approach's effectiveness and superiority are demonstrated on both real and synthetic networks.