  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.
