Binomial Tails for 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.

References in corpus (12)

• Scikit-learn: Machine Learning in Python
• Fast unfolding of communities in large networks
• Community structure in social and biological networks
• Community detection in graphs
• Fast algorithm for detecting community structure in networks
• Resolution limit in community detection
• Finding statistically significant communities in networks
• The ground truth about metadata and community detection in networks
• Significant Scales in Community Structure
• Detecting communities using asymptotical Surprise
• Centrality in Modular Networks
• A testing based extraction algorithm for identifying significant communities in networks