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

We propose a novel cohesive subgraph model called τ -strengthened (α , β) -core (denoted as (α , β) τ -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 τ butterflies (2 × 2 -bicliques). (α , β) τ -core requires each vertex on the upper or lower level to have at least α or β strong ties, given strength level τ. To retrieve the vertices of (α , β) τ -core optimally, we construct index I α , β , τ to store all (α , β) τ -cores. Effective optimization techniques are proposed to improve index construction. To make our idea practical on large graphs, we propose 2D-indexes I α , β , I β , τ , and I α , τ that selectively store the vertices of (α , β) τ -core for some α , β , and τ. The 2D-indexes are more space-efficient and require less construction time, each of which can support (α , β) τ -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) (α , β) τ -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. [ABSTRACT FROM AUTHOR]