Truss-based Community Search: a Truss-equivalence Based Indexing Approach

We consider the community search problem defined upon a large graph G: given a query vertex q in G, to find as output all the densely connected subgraphs of G, each of which contains the query v. As an online, query-dependent variant of the well-known community detection problem, community search enables personalized community discovery that has found widely varying applications in real-world, large-scale graphs. In this paper, we study the community search problem in the truss-based model aimed at discovering all dense and cohesive k-truss communities to which the query vertex q belongs. We introduce a novel equivalence relation, k-truss equivalence, to model the intrinsic density and cohesiveness of edges in k-truss communities. Consequently, all the edges of G can be partitioned to a series of k-truss equivalence classes that constitute a space-efficient, truss-preserving index structure, EquiTruss. Community search can be henceforth addressed directly upon EquiTruss without repeated, time-demanding accesses to the original graph, G, which proves to be theoretically optimal. In addition, EquiTruss can be efficiently updated in a dynamic fashion when G evolves with edge insertion and deletion. Experimental studies in real-world, large-scale graphs validate the efficiency and effectiveness of EquiTruss, which has achieved at least an order of magnitude speedup in community search over the state-of-the-art method, TCP-Index.