Recently, the topic of community search (CS) has gained plenty of attention. Given a query vertex, CS looks for a dense subgraph that contains it. Existing studies mainly focus on homogeneous graphs in which vertices are of the same type, and cannot be directly applied to heterogeneous information networks (HINs) that consist of multi-typed, interconnected objects, such as the bibliographic networks and knowledge graphs. In this paper, we study the problem of community search over large HINs; that is, given a query vertex q , find a community from an HIN containing q , in which all the vertices are with the same type of q and have close relationships. To model the relationship between two vertices of the same type, we adopt the well-known concept of meta-path , which is a sequence of relations defined between different types of vertices. We then measure the cohesiveness of the community by extending the classic minimum degree metric with a meta-path. We further propose efficient query algorithms for finding communities using these cohesiveness metrics. We have performed extensive experiments on five real large HINs, and the results show that the proposed solutions are effective for searching communities. Moreover, they are much faster than the baseline solutions.

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A bipartite network is a network with two disjoint vertex sets and its edges only exist between vertices from different sets. It has received much interest since it can be used to model the relationship between two different sets of objects in many applications (e.g., the relationship between users and items in E-commerce). In this paper, we study the problem of efficient bi-triangle counting for a large bipartite network, where a bi-triangle is a cycle with three vertices from one vertex set and three vertices from another vertex set. Counting bi-triangles has found many real applications such as computing the transitivity coefficient and clustering coefficient for bipartite networks. To enable efficient bi-triangle counting, we first develop a baseline algorithm relying on the observation that each bi-triangle can be considered as the join of three wedges. Then, we propose a more sophisticated algorithm which regards a bi-triangle as the join of two super-wedges, where a wedge is a path with two edges while a super-wedge is a path with three edges. We further optimize the algorithm by ranking vertices according to their degrees. We have performed extensive experiments on both real and synthetic bipartite networks, where the largest one contains more than one billion edges, and the results show that the proposed solutions are up to five orders of magnitude faster than the baseline method.

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