二部图中具有顶点接触和连接强度的凝聚子图的探索
Exploring Cohesive Subgraphs with Vertex Engagement and Tie Strength in Bipartite Graphs
摘要：
提出了一种新的凝聚子图模型$τ$ -enhanced $(α,β)$ -core（记为$(α,β)_τ$ -core），它是第一个同时考虑二部图上的结点连接强度和结点接合的凝聚子图模型.如果至少包含在$τ$蝴蝶（$2\times2$ -bicliques）中，则边是强连接。$(α,β)_τ$ -核心要求在给定强度级别$τ$的情况下，上层或下层的每个顶点至少具有$α$或$β$强关系。为了最优地检索$(α,β)_τ$ -核的顶点，我们构造了索引$I_{α,β,τ}$来存储所有的$(α,β)_τ$ -核.提出了有效的优化技术，以改善索引的建设。为了使我们的想法在大型图上实用，我们提出了二维索引$I_{α,β}, I_{β,τ}$和$I_{α,τ}$，它们选择性地存储某些$α,β$和$τ$的$(α,β)_τ$ -核心的顶点。二维索引具有更高的空间效率，需要更少的构建时间，每个索引都可以支持$(α,β)_τ$核心查询。由于查询效率取决于输入参数和二维索引的选择，我们提出了一个基于学习的混合计算范式，通过训练前馈神经网络来预测最佳的二维索引选择，最大限度地减少查询时间。大量实验表明，（$1$）$(α,β)_τ$ -core是一种有效的模型，能够捕捉到唯一且重要的内聚子图;（$2$）所提出的技术显著提高了索引构建和查询处理的效率.
英文摘要：
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 ($2\times2$-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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