Quantifying the presence/absence of meso-scale structures in networks

TL;DR

This paper introduces a Bayesian method to quantify and analyze meso-scale structures like communities and core-periphery in networks, providing probabilistic insights and uncertainty estimates, with applications to real-world data.

Contribution

It offers formal definitions and a Bayesian framework for detecting and quantifying meso-scale structures in networks, including uncertainty quantification.

Findings

Probabilistic statements about network structures.

Application to real-world networks reveals new insights.

Provides uncertainty estimates for group labels and edge probabilities.

Abstract

Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative communities, disassortative communities and core-periphery. We then leverage these definitions and a Bayesian framework to quantify the presence/absence of each structure in a network. This allows for probabilistic statements about the network structure as well as uncertainty estimates of the group labels and edge probabilities. The method is applied to real-world networks, yielding provocative results about well-known network data sets.