Finding Introverted Cores in Bipartite Graphs.

In this paper, we propose a novel cohesive subgraph model to find introverted communities in bipartite graphs, named ( α , β , p ) -core. It is a maximal subgraph in which every vertex in one part has at least α neighbors and at least p fraction of its neighbors in the subgraph, and every vertex in the other part has at least β neighbors. Compared to the ( α , β ) -core, the additional requirement on the fraction of neighbors in our model ensures that the vertices are introverted in the subgraph regarding their neighbor sets, e.g., for the ( α , β ) -core of a customer-product network, the shopping interests of the customers inside focus on the products in the subgraph. We propose an O ( m ) algorithm to compute the ( α , β , p ) -core with given α , β and p . Besides, we introduce an efficient algorithm to decompose a graph by the ( α , β , p ) -core. The experiments on real-world data demonstrate that our model is effective and our proposed algorithms are efficient.