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

Giulia Preti, Matteo Riondato, Aristides Gionis, Gianmarco De Francisci Morales
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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.
北极星从多图谱配置模型中采样,规定颜色同类性
我们介绍的 Polaris 是一种保留了联合颜色矩阵的彩色多图网络空模型。Polaris 是专为研究网络极化而设计的,其中顶点属于辩论中的一方或党派,用顶点颜色表示,而关系具有不同的强度,用整数值的边倍率表示。Polaris 的主要特点是保留多图的联合颜色矩阵(JCM),它规定了连接任意两种给定颜色顶点的边的数量。联合颜色矩阵是决定颜色同类性的基本属性,是研究极化网络中同质性和隔离性的一个基本方面。通过使用 Polaris,网络科学家们可以检验一种现象是否完全可以用观察到的网络的 JCM 来解释,或者是否有其他现象在起作用。从技术上讲,我们的空模型是配置模型的扩展:由具有相同度序列和相同 JCM 的彩色多图组成的集合。为了从这个集合中采样,我们开发了一套马尔可夫链蒙特卡洛算法,统称为 Polaris-*。它包括 Polaris-B(通用 Metropolis-Hastings 算法的改编版)和 Polaris-C(速度更快、接受概率更高的专用算法)。这一新的空模型和相关算法为研究社交网络中的极化现象提供了一个更细致的工具集,从而能够得出统计上合理的结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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