Community Detection and Improved Detectability in Multiplex Networks

Belief propagation is a technique to optimize probabilistic graphical models, and has been used to solve the community detection problem for networks described by the stochastic block model. In this work, we investigate the community detection problem in multiplex networks with generic community label constraints using the belief propagation algorithm. Our main contribution is a generative model that does not assume consistent communities between layers and allows a potentially heterogeneous community structure, suitable in many real world multiplex networks, such as social networks. We show by numerical experiments that in the presence of consistent communities between different layers, consistent communities are matched, and the detectability is improved over single layers. We compare it with a "correlated model" which has the prior knowledge of community correlation between layers. Similar detectability improvement is obtained, even though our model has much milder assumptions than the "correlated model". When the network has heterogeneous community structures, our model is shown to yield a better detection performance over a certain parameter range