Community detection in multiplex continous weighted nodes networks using an extension of the stochastic block model

The stochastic block model (SBM) is a probabilistic model aimed at clustering individuals within a simple network based on their social behavior. This network consists of individuals and edges representing the presence or absence of relationships between each pair of individuals. This paper aims to extend the traditional stochastic block model to accommodate multiplex weighted nodes networks. These networks are characterized by multiple relationship types occurring simultaneously among network individuals, with each individual associated with a weight representing its influence in the network. We introduce an inference method utilizing a variational expectation-maximization algorithm to estimate model parameters and classify individuals. Finally, we demonstrate the effectiveness of our approach through applications using simulated and real data, highlighting its main characteristics.