Significant Communities in Large Sparse Networks

Abstract

Researchers use community-detection algorithms to reveal large-scale organization in biological and social networks, but community detection is useful only if the communities are significant and not a result of noisy data. To assess the statistical significance of the network communities, or the robustness of the detected structure, one approach is to perturb the network structure by removing links and measure how much the communities change. However, perturbing sparse networks is challenging because they are inherently sensitive; they shatter easily if links are removed. Here we propose a simple method to perturb sparse networks and assess the significance of their communities. We generate resampled networks by adding extra links based on local information, then we aggregate the information from multiple resampled networks to find a coarse-grained description of significant clusters. In addition to testing our method on benchmark networks, we use our method on the sparse network of the European Court of Justice (ECJ) case law, to detect significant and insignificant areas of law. We use our significance analysis to draw a map of the ECJ case law network that reveals the relations between the areas of law.

The Politics of Citations at the ECJ—Policy Preferences of E.U. Member State Governments and the Citation Behavior of Judges at the European Court of Justice

“…One notable recent study attempts to provide empirical evidence on the implications of references to courts from other jurisdictions (Gelter & Siems 2014). Studies from the United States using network analysis seem to have triggered similar studies on courts outside the United States (Lupu & Voeten 2011;Tarissan & Nollez-Goldbach 2014), including the ECJ (Derl en et al 2013;Derl en & Lindholm 2014;Mirshahvalad et al 2012;Sadl & Hink 2014). However, so far, studies on the citation behavior of the members of the ECJ have not considered the political background of judges.…”

To cut or not to cut? Assessing the modular structure of brain networks

“…Hu et al (2010) offered a generalization to this approach by incorporating together the number of clusters, content of the clusters, and random perturbation parameters. Mirshahvalad et al (2012) studied the robustness of large sparse networks by randomly adding extra links based on local information. Lancichinetti et al (2010) evaluated the importance of single communities using combinatorics and a modified null model.…”

Parametric distributions for assessing significance in modular partitions of brain networks

“…A number of approaches have been proposed to deal with this problem by using small perturbations or resampling of edges [4,5], eigenvalue distribution modeling [6,7], or the Potts spin-glass model [8].…”