Hurricane in Bipartite Graphs: The Lethal Nodes of Butterflies

Qiuyu Zhu, Jiahong Zheng, Han Yang, Chen Chen, Xiaoyang Wang, Ying Zhang
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引用次数: 12

Abstract

Bipartite graphs are widely used when modeling the relationships between two different types of entities, such as purchase relationships. In a bipartite graph, the number of butterflies, i.e., 2 × 2 biclique, is a fundamental metric for analyzing the structures and properties of bipartite graphs. Considering the deletion of critical nodes may affect the stability of bipartite graphs, we propose the butterfly minimization problem, where the attacker aims to maximize the number of butterflies removed from the graph by deleting b nodes. We prove the problem is NP-hard, and the objective function is monotonic and submodular. We adopt a greedy algorithm to solve the problem with 1 − 1/e approximation ratio. To scale for large graphs, novel methods are developed to reduce the searching space. Experiments over real-world bipartite graphs are conducted to demonstrate the advantages of proposed techniques.
二部图中的飓风:蝴蝶的致命节点
二部图在对两种不同类型的实体之间的关系进行建模时被广泛使用,例如购买关系。在二部图中,蝶形数即2 × 2双方数是分析二部图结构和性质的基本度量。考虑到关键节点的删除可能会影响二部图的稳定性,我们提出了蝴蝶最小化问题,攻击者的目标是通过删除b个节点来最大化从图中移除的蝴蝶数量。我们证明了这个问题是np困难的,并且目标函数是单调的和次模的。我们采用贪心算法求解1−1/e近似比的问题。为了对大型图进行缩放,开发了新的方法来减少搜索空间。在真实世界的二部图上进行了实验,以证明所提出的技术的优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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