Exploring the structural regularities in networks

TL;DR

This paper introduces a flexible statistical model for analyzing network structures, capable of identifying various regularities such as communities and multipartite patterns without prior assumptions.

Contribution

It presents a unified, highly adaptable model that learns different network regularities directly from data, surpassing existing models in detecting diverse structures.

Findings

Model outperforms state-of-the-art in real and artificial networks.

Detects overlapping communities and multipartite structures.

Identifies multiple structural regularities beyond existing models.

Abstract

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically, we propose a general statistical model to describe network structure. In this model, group is viewed as hidden or unobserved quantity and it is learned by fitting the observed network data using the expectation-maximization algorithm. Compared with existing models, the most prominent strength of our model is the high flexibility. This strength enables it to possess the advantages of existing models and overcomes their shortcomings in a unified way. As a result, not only broad types of structure can be detected without prior knowledge of what type of intrinsic regularities exist in the network, but also the type of identified structure can be directly learned from data. Moreover, by differentiating outgoing edges from incoming edges, our model can detect several types of structural regularities beyond competing models. Tests on a number of real world and artificial networks demonstrate that our model outperforms the state-of-the-art model at shedding light on the structural features of networks, including the overlapping community structure, multipartite structure and several other types of structure which are beyond the capability of existing models.