Index-Based Intimate-Core Community Search in Large Weighted Graphs

Longxu Sun, Xin Huang, Rong-Hua Li, Byron Choi, Jianliang Xu

Abstract: Community search that finds query-dependent communities has been studied on various kinds of graphs. As one instance of community search, intimate-core group (community) search over a weighted graph is to find a connected $k$ -core containing all query nodes with the smallest group weight. However, existing state-of-the-art methods start from the maximal $k$ -core to refine an answer, which is practically inefficient for large networks. In this paper, we develop an efficient framework, called l ocal e xploration k -core s earch (LEKS), to find intimate-core groups in graphs. We propose a small-weighted spanning tree to connect query nodes, and then expand the tree level by level to a connected $k$ -core, which is finally refined as an intimate-core group. In addition, to support the intimate group search over large weighted graphs, we develop a weighted-core index (WC-index) and two new WC-index-based algorithms for expansion and refinement phases in LEKS. Specifically, we propose a WC-index-based expansion to efficiently find a candidate graph of intimate-core group, leveraging on a two-level expansion of $k$ -breadth and 1-depth. We propose two graph removal strategies: coarse-grained refinement is designed for large graphs to delete a batch of nodes in a few iterations; fine-grained refinement is designed for small graphs to remove nodes carefully and achieve high-quality answers. Extensive experiments on real-life networks with ground-truth communities validate the effectiveness and efficiency of our proposed methods.