A unifying framework for fast randomization of ecological networks with fixed (node) degrees

TL;DR

This paper introduces Curveball algorithms for simple directed and undirected graphs that perform trades to efficiently generate random graphs with fixed degree sequences, outperforming traditional switching models in convergence speed.

Contribution

It extends the Curveball algorithm to simple graphs and demonstrates faster convergence compared to existing switching models.

Findings

Curveball algorithms converge faster than switching models

Single and simultaneous trades improve sampling efficiency

Algorithms effectively generate uniform samples of fixed-degree graphs

Abstract

The switching model is a Markov chain approach to sample graphs with fixed degree sequence uniformly at random. The recently invented Curveball algorithm for bipartite graphs applies several switches simultaneously (`trades'). Here, we introduce Curveball algorithms for simple (un)directed graphs which use single or simultaneous trades. We show experimentally that these algorithms converge magnitudes faster than the corresponding switching models.