Combinatorial Miller-Hagberg Algorithm for Randomization of Dense Networks

TL;DR

This paper introduces a revised Miller-Hagberg algorithm that uses combinatorial calculations to improve the accuracy of network randomization, especially for dense networks with high-degree nodes, while maintaining computational efficiency.

Contribution

A modified Miller-Hagberg algorithm employing combinatorial edge probabilities for better dense network randomization, with comparable computational complexity to the original.

Findings

Accurately models high-degree nodes in dense networks

Maintains similar computational complexity as original algorithm

Effective for large, dense, heterogeneous networks

Abstract

We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a combinatorically calculated edge probability that better captures the likelihood of edge presence especially where edges are dense. The computational complexity of this combinatorial MH algorithm is still in the same order as the original one. We evaluated the proposed algorithm through several numerical experiments. The results demonstrated that the proposed algorithm was particularly good at accurately representing high-degree nodes in dense, heterogeneous networks. This algorithm may be a useful alternative of other more established network randomization methods, given that the data are increasingly becoming larger and denser in today's network science research.