Dense subgraphs in temporal social networks

Interactions among entities are usually modeled using graphs. In many real scenarios, these relations may change over time, and different kinds exist among entities that need to be integrated. We introduce a new network model called temporal dual network, to deal with interactions which change over time and to integrate information coming from two different networks. In this new model, we consider a fundamental problem in graph mining, that is, finding the densest subgraphs. To deal with this problem, we propose an approach that, given two temporal graphs, (1) produces a dual temporal graph via alignment and (2) asks for identifying the densest subgraphs in this resulting graph. For this latter problem, we present a polynomial-time dynamic programming algorithm and a faster heuristic based on constraining the dynamic programming to consider only bounded temporal graphs and a local search procedure. We show that our method can output solutions not far from the optimal ones, even for temporal graphs having 10000 vertices and 10000 timestamps. Finally, we present a case study on a real dual temporal network.