Stochastic Block Models for Multiplex Networks: An Application to a Multilevel Network of Researchers
将随机块模型扩展到多重网络，通过变分期望最大化估计参数，并用集成完成似然准则选择分组数，应用于法国癌症研究人员网络，揭示直接联系和实验室联系两种关系下的群体结构。
Summary Modelling relationships between individuals is a classical question in social sciences and clustering individuals according to the observed patterns of interactions allows us to uncover a latent structure in the data. The stochastic block model is a popular approach for grouping individuals with respect to their social comportment. When several relationships of various types can occur jointly between individuals, the data are represented by multiplex networks where more than one edge can exist between the nodes. We extend stochastic block models to multiplex networks to obtain a clustering based on more than one kind of relationship. We propose to estimate the parameters—such as the marginal probabilities of assignment to groups (blocks) and the matrix of probabilities of connections between groups—through a variational expectation–maximization procedure. Consistency of the estimates is studied. The number of groups is chosen by using the integrated completed likelihood criterion, which is a penalized likelihood criterion. Multiplex stochastic block models arise in many situations but our applied example is motivated by a network of French cancer researchers. The two possible links (edges) between researchers are a direct connection or a connection through their laboratories. Our results show strong interactions between these two kinds of connection and the groups that are obtained are discussed to emphasize the common features of researchers grouped together.