Community detection in networks is a useful tool for detecting the behavioral and inclinations of users to a specific topic or title. Weighted, unweighted, directed, and undirected networks can all be used for detecting communities depending on the network structure and content. The proposed model framework for community detection is based on weighted networks. We use two important and effective concepts in graph analysis. The structural density between nodes is the first concept, and the second is the weight of edges between nodes. The proposed model advantage is using a probabilistic generative model that estimates the latent parameters of the probabilistic model and detecting the community based on the probability of the presence or absence of weighted edge. The output of the proposed model is the intensity of belonging each weighted node to the communities. A relationship between the observation of a pair of nodes in multiple communities and the probability of an edge with a high weight between them, is one of the important outputs that interpret the detected communities by finding relevancy between membership of nodes to communities and edge weight. Experiments are performed on real-world weighted networks and synthetic weighted networks to evaluate the performance and accuracy of the proposed algorithm. The results will show that the proposed algorithm is more density and accurate than other algorithms in weighted community detection.

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.