Centrality metrics are one of the most fundamental tools in social network analysis and network science, and various measures for evaluating node importance metrics have been devised. However, the crucial issue of testing the discriminating power of different centrality measures is still open. In this article, we propose to assess the discriminating power of node centrality measures by using the notion of automorphism and orbit: nodes in the same orbit have identical metric scores, while nodes in different orbits should have different centrality values. Under this assumption, we present a benchmark for the discriminating power of node centrality measures. Moreover, we propose an efficient approach to evaluate centrality measures in terms of the discriminating power, which is devoid of finding orbits. Extensive experiments on real and model networks are executed to compare seven commonly used node centrality metrics.

中文翻译：

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复杂网络中中心性度量的判别力


中心性度量是社交网络分析和网络科学中最基本的工具之一，并且已经设计了各种评估节点重要性度量的方法。然而，测试不同中心性度量的区分力的关键问题仍然悬而未决。在本文中，我们建议使用自同构和轨道的概念来评估节点中心性度量的判别力：同一轨道中的节点具有相同的度量分数，而不同轨道中的节点应具有不同的中心性值。在这个假设下，我们提出了节点中心性度量的区分能力的基准。此外，我们提出了一种根据判别力评估中心性度量的有效方法，该方法无需寻找轨道。在真实网络和模型网络上进行了大量实验，以比较七种常用的节点中心性指标。