基于中心性的顶点移除后随机图的连通性
Connectivity of random graphs after centrality-based vertex removal
AI总结：
本文研究移除中心顶点对网络连通性的影响，利用局部收敛技术分析连通分量极限数量并证明巨分量大小上界，在配置模型中证明移除最高度顶点对巨分量破坏最大。
摘要：
中心性度量旨在指示网络中谁更重要。不同的“重要性”概念产生了不同的中心性度量。本文通过研究移除最重要中心顶点如何影响连通分量数量和巨分量大小，探讨了中心顶点对网络连通结构的重要性。我们使用局部收敛技术，为局部收敛图和依赖于顶点邻域的中心性度量，识别出连通分量的极限数量。对于巨分量大小，我们证明了一个一般上界。为得到匹配下界，我们专门研究了网络科学中最流行模型之一的配置模型上的度中心性情况，并表明移除最高度顶点对巨分量的破坏最大。
英文摘要：
Centrality measures aim to indicate who is important in a network. Various notions of `being important' give rise to different centrality measures. In this paper, we study how important the central vertices are for the connectivity structure of the network, by investigating how the removal of the most central vertices affects the number of connected components and the size of the giant component. We use local convergence techniques to identify the limiting number of connected components for locally converging graphs and centrality measures that depend on the vertex's neighborhood. For the size of the giant, we prove a general upper bound. For the matching lower bound, we specialize to the case of degree centrality on one of the most popular models in network science, the configuration model, for which we show that removal of the highest-degree vertices destroys the giant most.
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