论文标题
针对有向网络的拓扑中心度度量
A Topological Centrality Measure for Directed Networks
论文作者
论文摘要
鉴于有指导的网络$ g $，我们有兴趣研究$ g $的定性功能，这些特征控制着$ g $的扰动如何传播。已经制定了各种经典的中心度度量，并证明可用于捕获无向网络的定性特征和行为。在本文中，我们使用拓扑数据分析（TDA）来适应中心度度量，以捕获网络中的定向性和非本地传播行为。我们引入了一个新的指标，用于计算有向加权网络中的中心性，即准中心度量。我们计算在贸易网络上的这些指标，以说明我们的度量成功捕获了网络中的传播效果，还可以用于识别可能破坏定向网络拓扑的冲击源。此外，我们介绍了一种方法，该方法对有向网络中节点的拓扑影响提供了层次结构表示。
Given a directed network $ G $, we are interested in studying the qualitative features of $ G $ which govern how perturbations propagate across $ G $. Various classical centrality measures have been already developed and proven useful to capture qualitative features and behaviors for undirected networks. In this paper, we use topological data analysis (TDA) to adapt measures of centrality to capture both directedness and non-local propagating behaviors in networks. We introduce a new metric for computing centrality in directed weighted networks, namely the quasi-centrality measure. We compute these metrics on trade networks to illustrate that our measure successfully captures propagating effects in the network and can also be used to identify sources of shocks that can disrupt the topology of directed networks. Moreover, we introduce a method that gives a hierarchical representation of the topological influences of nodes in a directed network.
