Exploring cohesive subgraphs with vertex engagement and tie strength in bipartite graphs

We propose a novel cohesive subgraph model called tau-strengthened (alpha,beta)-core (denoted as (alpha,beta)(tau)-core), which is the first to consider both tie strength and vertex engagement on bipartite graphs. An edge is a strong tie if contained in at least tau butterflies (2 x 2-bicliques). (alpha,beta)(tau)-core requires each vertex on the upper or lower level to have at least alpha or beta strong ties, given strength level tau. To retrieve the vertices of (alpha,beta)(tau)-core optimally, we construct index I-alpha,I-beta,I-tau to store all (alpha,beta)(tau)-cores. Effective optimization techniques are proposed to improve index construction. To make our idea practical on large graphs, we propose 2D-indexes lap I-alpha,I-beta, I-beta,I-tau, and I-alpha,I-tau that selectively store the vertices of (alpha,beta)(tau)-core for some alpha, beta, and tau. The 2D-indexes are more space-efficient and require less construction time, each of which can support (alpha,beta)(tau)-core queries. As query efficiency depends on input parameters and the choice of 2D-index, we propose a learning-based hybrid computation paradigm by training a feed-forward neural network to predict the optimal choice of 2D-index that minimizes the query time. Extensive experiments show that (1) (alpha,beta)(tau)-core is an effective model capturing unique and important cohesive subgraphs; (2) the proposed techniques significantly improve the efficiency of index construction and query processing. (C) 2021 Elsevier Inc. All rights reserved.