A motif-based probabilistic approach for community detection in complex networks

Community detection in complex networks is an important task for discovering hidden information in network analysis. Neighborhood density between nodes is one of the fundamental indicators of community presence in the network. A community with a high edge density will have correlations between nodes that extend beyond their immediate neighbors, denoted by motifs. Motifs are repetitive patterns of edges observed with high frequency in the network. We proposed the PCDMS method (Probabilistic Community Detection with Motif Structure) that detects communities by estimating the triangular motif in the network. This study employs structural density between nodes, a key concept in graph analysis. The proposed model has the advantage of using a probabilistic generative model that calculates the latent parameters of the probabilistic model and determines the community based on the likelihood of triangular motifs. The relationship between observing two pairs of nodes in multiple communities leads to an increasing likelihood estimation of the existence of a motif structure between them. The output of the proposed model is the intensity of each node in the communities. The efficiency and validity of the proposed method are evaluated through experimental work on both synthetic and real-world networks; the findings will show that the community identified by the proposed method is more accurate and dense than other algorithms with modularity, NMI, and F1score evaluation metrics.