Exploring Cohesive Subgraphs with Vertex Engagement and Tie Strength in Bipartite Graphs
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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.
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