Quantifying structure in networks

TL;DR

This paper explores exponential family models for undirected, unlabeled networks to systematically quantify their structure, focusing on subgraph counts and dependencies among common network observables.

Contribution

It introduces a framework using exponential families to analyze network structure through subgraph counts and observable dependencies, advancing systematic quantification methods.

Findings

Subgraph counts with up to k links serve as sufficient statistics.

Dependencies among degree distribution, clustering, and assortativity are analyzed.

Framework applies to undirected unlabeled graphs.

Abstract

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.