Community detection, link prediction, and layer interdependence in multilayer networks

摘要

Complex systems are often characterized by distinct types of interactions between the same entities. Thesecan be described as a multilayer network where each layer represents one type of interaction. These layers maybe interdependent in complicated ways, revealing different kinds of structure in the network. In this work wepresent a generative model, and an efficient expectation-maximization algorithm, which allows us to performinference tasks such as community detection and link prediction in this setting. Our model assumes overlappingcommunities that are common between the layers, while allowing these communities to affect each layer ina different way, including arbitrary mixtures of assortative, disassortative, or directed structure. It also givesus a mathematically principled way to define the interdependence between layers, by measuring how muchinformation about one layer helps us predict links in another layer. In particular, this allows us to bundle layerstogether to compress redundant information and identify small groups of layers which suffice to predict theremaining layers accurately. We illustrate these findings by analyzing synthetic data and two real multilayernetworks, one representing social support relationships among villagers in South India and the other representingshared genetic substring material between genes of the malaria parasite.