Binomial Tails for Community Analysis
This work provides a more robust method for ranking and filtering discovered communities in networks, which is beneficial for analysts working with community discovery.
This paper addresses the challenge of assessing the significance and robustly ranking candidate communities discovered in networks. The authors develop efficient group scoring functions based on binomial tail probabilities, demonstrating that this approach leads to more robust rankings compared to other inexpensive methods like conductance.
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.