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

TL;DR

This paper introduces a generative model and an EM algorithm for community detection and link prediction in multilayer networks, capturing complex interdependencies and layer-specific structures.

Contribution

It presents a novel probabilistic framework that models overlapping communities across layers and quantifies interlayer interdependence for improved inference.

Findings

Effective inference of communities and links in multilayer networks.

Identification of layer groups that can predict other layers.

Application to social and biological multilayer networks demonstrates utility.

Abstract

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