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.