Abstract

Random networks have been widely used to describe interactions between objects, including interpersonal relationships among individuals. One of the most important features of networks is the presence of communities, which are groups of nodes with similar connection patterns. In this regard, we propose a model in which edges between pairs of vertices are randomly assigned, given the communities of those vertices, following the zero-inflated Poisson (ZIP) distribution. This proposal allows us to model networks with community structures that are sparse and have weighted edges.

The estimation of the ZIP distribution parameters is performed using the EM algorithm, while the estimation of communities is done using the EM-Variational algorithm. The performance of the estimators is evaluated through simulation studies, using the Normalized Mutual Information (NMI) measure to compare the true and estimated communities. To compare the estimated parameters of the ZIP distribution, we use the Mean Squared Error (MSE).

Finally, we apply the proposed model to airport networks in Brazil and detect the community structure from 2018 to 2021 to evaluate the changes that occurred in these networks before and during the COVID-19 pandemic period. The application of the model to real data demonstrated its effectiveness in detecting communities and analyzing structural changes in complex networks. Thus, we believe our approach can significantly contribute to the advancement of community detection.