Sampling motif-constrained ensembles of networks

TL;DR

This paper introduces a novel multicanonical sampling method using Wang-Landau to efficiently generate network ensembles with specified motif constraints, overcoming limitations of traditional exponential random graph models.

Contribution

The authors develop a polynomial-time sampling approach for networks with prescribed motif counts, addressing sampling and inconsistency issues in existing models.

Findings

Efficient sampling of networks with motif constraints

Quantified the correlation between motifs in social networks

Single motifs can explain up to 60% of motif profile variation

Abstract

The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency, or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this paper we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, net- works with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60% of the variation of motif profiles.