Efficient Triangle-Connected Truss Community Search in Dynamic Graphs

Abstract

Community search studies the retrieval of certain community structures containing query vertices, which has received lots of attention recently. k -truss is a fundamental community structure where each edge is contained in at least k - 2 triangles. Triangle-connected k -truss community ( k -TTC) is a widely-used variant of k -truss, which is a maximal k -truss where edges can reach each other via a series of edge-adjacent triangles. Although existing works have provided indexes and query algorithms for k -TTC search, the cohesiveness of a k -TTC (diameter upper bound) has not been theoretically analyzed and the triangle connectivity has not been efficiently captured. Thus, we revisit the k -TTC search problem in dynamic graphs, aiming to achieve a deeper understanding of k -TTC. First, we prove that the diameter of a k -TTC with n vertices is bounded by [EQUATION]. Then, we encapsulate triangle connectivity with two novel concepts, partial class and truss-precedence, based on which we build our compact index, EquiTree, to support the efficient k -TTC search. We also provide efficient index construction and maintenance algorithms for the dynamic change of graphs. Compared with the state-of-the-art methods, our extensive experiments show that EquiTree can boost search efficiency up to two orders of magnitude at a small cost of index construction and maintenance.