Unstable communities in network ensembles

Ensembles of graphs arise in several natural applications. Many techniques exist to compute frequent, dense subgraphs in these ensembles. In contrast, in this paper, we propose to discover maximally variable regions of the graphs, i.e., sets of nodes that induce very different subgraphs across the ensemble. We first develop two intuitive and novel definitions of such node sets, which we then show can be efficiently enumerated using a level-wise algorithm. Finally, using extensive experiments on multiple real datasets, we show how these sets capture the main structural variations of the given set of networks and also provide us with interesting and relevant insights about these datasets.