Estimation in a Binomial Stochastic Blockmodel for a Weighted Graph by a Variational Expectation Maximization Algorithm

Stochastic blockmodels have been widely proposed as a probabilistic random graph model for the analysis of networks data as well as for detecting community structure in these networks. In a number of real-world networks, not all ties among nodes have the same weight. Ties among networks nodes are often associated with weights that differentiate them in terms of their strength, intensity, or capacity. In this paper, we provide an inference method through a variational expectation maximization algorithm to estimate the parameters in binomial stochastic blockmodels for weighted networks. To prove the validity of the method and to highlight its main features, we set some applications of the proposed approach on some simulated data and some real data sets. Stochastic blockmodels belong to latent classes models. Classes defines a node’s clustering. We compare the clustering found through binomial stochastic blockmodels with the ones found fitting a stochasticblockmodel with Poisson distributed edges. Inferred Poisson and binomial stochastic blockmodels mainly differs. Moreover, in our examples, the statistical error is lower for binomial stochastic blockmodels