Inferring the mesoscale structure of layered, edge-valued and time-varying networks

TL;DR

This paper introduces a robust Bayesian method for inferring mesoscale structures in complex layered, attributed, and time-varying networks, enabling better understanding of their hidden modular organization.

Contribution

It presents a novel nonparametric Bayesian framework for modeling and inferring the structure of multi-dimensional networks, addressing overfitting and model selection challenges.

Findings

Successfully reveals hidden structures in diverse empirical networks.

Identifies the most appropriate granularity for additional network dimensions.

Demonstrates robustness across social, political, transportation, and proximity networks.

Abstract

Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a time-dependence of the network structure. Although they are crucial for a more comprehensive scientific understanding, these representations offer substantial challenges. Namely, it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects. Furthermore, the direct incorporation of these features invariably increases the effective dimension of the network description, and hence aggravates the problem of overfitting, i.e. the use of overly-complex characterizations that mistake purely random fluctuations for actual structure. In this work, we propose a robust and principled method to tackle these problems, by constructing generative models of modular network structure, incorporating layered, attributed and time-varying properties, as well as a nonparametric Bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence. We show that the method is capable of revealing hidden structure in layered, edge-valued and time-varying networks, and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified. We illustrate our approach on a variety of empirical systems, including a social network of physicians, the voting correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.