We describe a methodology for characterizing the relative structural importance of an arbitrary network edge by exploiting the properties of a k-shortest path algorithm. We introduce the metric Edge Gravity, measuring how often an edge occurs in any possible network path, as well as k-Gravity, a lower bound based on paths enumerated while solving the k-shortest path problem. The methodology is demonstrated using Granovetter’s original strength of weak ties network examples as well as the well-known Florentine families of the Italian Renaissance and the Krebs 2001 terrorist networks. The relationship to edge betweenness is established. It is shown that important edges, i.e. ones with a high Edge Gravity, are not necessarily adjacent to nodes of importance as identified by standard centrality metrics, and that key nodes, i.e. ones with high centrality, often have their importance bolstered by being adjacent to bridges to nowhere–e.g. ones with low Edge Gravity. It is also demonstrated that Edge Gravity distinguishes critically important bridges or local bridges from those of lesser structural importance.

中文翻译：

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边缘的重力。

我们描述了一种通过利用k最短路径算法的特性来表征任意网络边缘的相对结构重要性的方法。我们引入度量“边缘引力”（Edge Gravity），测量边缘在任何可能的网络路径中出现的频率，以及k -Gravity，它是在解决k-最短路径问题时基于枚举路径的下限。该方法论是通过Granovetter弱连接网络示例的原始实力以及意大利文艺复兴和克雷布斯2001恐怖网络的著名佛罗伦萨家庭来证明的。建立与边缘之间的关系。结果表明重要的边缘，即具有较高边缘的边缘边缘重力不一定与标准中心度度量标准所标识的重要节点相邻，并且关键节点（即具有较高中心度的关键节点）的重要性通常是通过与无处相邻的桥（例如，边缘重力较低的那些）相邻来增强的。还表明，“边缘重力”可将至关重要的桥梁或局部桥梁与次要的桥梁区分开。