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

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