Neighborhood Structure Configuration Models

TL;DR

This paper introduces a novel method for generating synthetic networks that accurately preserve the local neighborhood structure of a given network, balancing diversity and structural fidelity, especially useful for large networks.

Contribution

The paper presents a colored Configuration Model using Color Refinement to efficiently sample networks with controllable neighborhood similarity, advancing network modeling techniques.

Findings

Synthetic networks become more similar to the original with more Color Refinement iterations.

The method effectively preserves centrality measures like PageRank and eigenvector centrality.

It enables controlled, scalable network sampling for large networks.

Abstract

We develop a new method to efficiently sample synthetic networks that preserve the d-hop neighborhood structure of a given network for any given d. The proposed algorithm trades off the diversity in network samples against the depth of the neighborhood structure that is preserved. Our key innovation is to employ a colored Configuration Model with colors derived from iterations of the so-called Color Refinement algorithm. We prove that with increasing iterations the preserved structural information increases: the generated synthetic networks and the original network become more and more similar, and are eventually indistinguishable in terms of centrality measures such as PageRank, HITS, Katz centrality and eigenvector centrality. Our work enables to efficiently generate samples with a precisely controlled similarity to the original network, especially for large networks.