Generative model for reciprocity and community detection in networks

TL;DR

This paper introduces a probabilistic generative model for directed networks that captures reciprocity and community structure, providing improved prediction and network generation capabilities over existing methods.

Contribution

It proposes a novel model that assigns community memberships and a reciprocity parameter, with an efficient EM algorithm for scalable inference, outperforming previous approaches.

Findings

Outperforms existing methods in edge prediction.

Accurately models reciprocity in real networks.

Infers meaningful community structures.

Abstract

We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community memberships to nodes and a reciprocity parameter to the whole network rather than fitting order statistics. It formalizes the assumption that a directed interaction is more likely to occur if an individual has already observed an interaction towards her. It provides a natural framework for relaxing the common assumption in network generative models of conditional independence between edges, and it can be used to perform inference tasks such as predicting the existence of an edge given the observation of an edge in the reverse direction. Inference is performed using an efficient expectation-maximization algorithm that exploits the sparsity of the network, leading to an efficient and scalable implementation. We illustrate these findings by analyzing synthetic and real data, including social networks, academic citations and the Erasmus student exchange program. Our method outperforms others in both predicting edges and generating networks that reflect the reciprocity values observed in real data, while at the same time inferring an underlying community structure. We provide an open-source implementation of the code online.