Generating constrained random graphs using multiple edge switches

TL;DR

This paper introduces a generalized method called "k-edge switching" for generating random graphs with constraints, improving coverage and representativeness of samples compared to traditional edge swap techniques.

Contribution

It proposes a novel higher-order edge switching approach to better explore constrained graph spaces, enhancing sampling reliability.

Findings

k-edge switching increases the set of accessible graphs

The method improves sampling uniformity over constrained graph sets

Asymptotic confidence in sample representativeness is achieved

Abstract

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily possible to access all graphs obeying some given con- straints through a classical switching procedure calling on pairs of edges. We therefore propose to get round this issue by generalizing this classical approach through the use of higher-order edge switches. This method, which we denote by "k-edge switching", makes it possible to progres- sively improve the covered portion of a set of constrained graphs, thereby providing an increasing, asymptotically certain confidence on the statistical representativeness of the obtained sample.