Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

TL;DR

This paper develops a mathematical framework for creating tailored random graph ensembles that match real network properties, enabling precise quantification and comparison of network structures beyond simple degree statistics.

Contribution

It introduces a family of graph ensembles with analytically controllable parameters that match real network degree distributions and correlations, facilitating advanced structural analysis.

Findings

Enables explicit calculation of entropies and complexities of network ensembles.

Provides formulas for information-theoretic distances between networks.

Offers tools for macro-level network topology comparison.

Abstract

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.