Binomial Tails for Community Analysis

TL;DR

This paper introduces binomial tail-based scoring functions for community detection in networks, providing a robust ranking method and confidence measures to evaluate the significance of discovered communities.

Contribution

It develops simple, efficient binomial tail probability-based scoring functions for community significance assessment, improving robustness over traditional methods.

Findings

Binomial scoring outperforms conductance in ranking communities.

Provides p-values for filtering and labeling communities.

Demonstrates versatility of binomial tail approach in community analysis.

Abstract

An important task of community discovery in networks is assessing significance of the results and robust ranking of the generated candidate groups. Often in practice, numerous candidate communities are discovered, and focusing the analyst's time on the most salient and promising findings is crucial. We develop simple efficient group scoring functions derived from tail probabilities using binomial models. Experiments on synthetic and numerous real-world data provides evidence that binomial scoring leads to a more robust ranking than other inexpensive scoring functions, such as conductance. Furthermore, we obtain confidence values ($p$-values) that can be used for filtering and labeling the discovered groups. Our analyses shed light on various properties of the approach. The binomial tail is simple and versatile, and we describe two other applications for community analysis: degree of community membership (which in turn yields group-scoring functions), and the discovery of significant edges in the community-induced graph.