Dense and well-connected subgraph detection in dual networks

Abstract

Dense subgraph discovery is a fundamental problem in graph mining whose goal is to extract a dense subgraph from a given graph, and it has a wide range of applications [18]. However, numerous real-world applications, ranging from computational biology and computational neuroscience to computational social science, take as input a dual graph, namely a pair of graphs on the same set of nodes. Despite the large number of such applications, research on dense subgraph discovery has focused on a single graph input, with few notable exceptions [9, 22, 35, 36]. In this work, we contribute to this line of research by studying the following novel algorithmic problem: Given a pair of graphs G, H on the same set of nodes V, how do we find a subset of nodes S ⊆ V that induces a well-connected subgraph in G and a dense subgraph in H? Our formulation generalizes previous research [11, 44, 45], by enabling to control the connectivity constraint on G. We propose a mathematical formulation and prove that it is solvable exactly in polynomial time. We compare our method to state-of-the-art competitors and find empirically that controlling the connectivity constraint enables the practitioner to obtain information that is otherwise inaccessible. Finally, we show that our proposed mining tool can be used to better understand how users interact on Twitter and connectivity aspects of human brain networks with and without Autism Spectrum Disorder (ASD).