Polaris: Sampling from the Multigraph Configuration Model with Prescribed Color Assortativity

TL;DR

Polaris is a null model for colored multigraphs that preserves the Joint Color Matrix, enabling better analysis of polarization and homophily in social networks through specialized sampling algorithms.

Contribution

We introduce Polaris, a novel null model for colored multigraphs that maintains the Joint Color Matrix and develop efficient MCMC algorithms for sampling from this model.

Findings

Polaris accurately preserves the Joint Color Matrix in sampled networks.

The algorithms enable statistically sound tests of polarization phenomena.

Polaris offers a nuanced tool for analyzing homophily and segregation in social networks.

Abstract

We introduce Polaris, a network null model for colored multi-graphs that preserves the Joint Color Matrix. Polaris is specifically designed for studying network polarization, where vertices belong to a side in a debate or a partisan group, represented by a vertex color, and relations have different strengths, represented by an integer-valued edge multiplicity. The key feature of Polaris is preserving the Joint Color Matrix (JCM) of the multigraph, which specifies the number of edges connecting vertices of any two given colors. The JCM is the basic property that determines color assortativity, a fundamental aspect in studying homophily and segregation in polarized networks. By using Polaris, network scientists can test whether a phenomenon is entirely explained by the JCM of the observed network or whether other phenomena might be at play. Technically, our null model is an extension of the configuration model: an ensemble of colored multigraphs characterized by the same degree sequence and the same JCM. To sample from this ensemble, we develop a suite of Markov Chain Monte Carlo algorithms, collectively named Polaris-*. It includes Polaris-B, an adaptation of a generic Metropolis-Hastings algorithm, and Polaris-C, a faster, specialized algorithm with higher acceptance probabilities. This new null model and the associated algorithms provide a more nuanced toolset for examining polarization in social networks, thus enabling statistically sound conclusions.