Edge centrality has found wide applications in various aspects. Many edge centrality metrics have been proposed, but the crucial issue that how good the discriminating power of a metric is, with respect to other measures, is still open. In this paper, we address the question about the benchmark of the discriminating power of edge centrality metrics. We first use the automorphism concept to define equivalent edges, based on which we introduce a benchmark for the discriminating power of edge centrality measures and develop a fast approach to compare the discriminating power of different measures. According to the benchmark, for a desirable measure, equivalent edges have identical metric scores, while inequivalent edges possess different scores. However, we show that even in a toy graph, inequivalent edges cannot be discriminated by three existing edge centrality metrics. We then present a novel edge centrality metric called forest centrality (FC). Extensive experiments on real-world networks and model networks indicate that FC has better discriminating power than three existing edge centrality metrics.

中文翻译：

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边缘中心性度量的判别能力基准

边缘中心性在各个方面都有广泛的应用。已经提出了许多边缘中心性度量，但是关于其他度量的度量的判别力有多好这个关键问题仍然悬而未决。在本文中，我们解决了关于边缘中心度度量的判别力基准的问题。我们首先使用自同构概念来定义等价边，在此基础上，我们引入了边中心性度量的判别力基准，并开发了一种快速方法来比较不同度量的判别力。根据基准，对于理想的度量，等效边具有相同的度量分数，而不等边具有不同的分数。然而，我们证明即使在玩具图中，三个现有的边缘中心性度量不能区分不等边。然后，我们提出了一种新的边缘中心度度量，称为森林中心度 (FC)。对现实世界网络和模型网络的大量实验表明，FC 比现有的三个边缘中心度指标具有更好的判别能力。