杠杆中心性的图论分析
A Graph Theoretic Analysis of Leverage Centrality
摘要：
2010年，Joyce et. Al将图中顶点的杠杆中心性定义为分析人脑内功能连接的一种手段。在这个度量中，一个顶点的度与它所有邻居的度进行比较。我们从数学的角度研究这个属性。我们首先概述了一些基本性质，然后计算杠杆中心的顶点在不同的家庭的图。特别是，我们发现有一个令人惊讶的连接之间的数量不同的杠杆中心的笛卡儿积的路径和三角形的数量。
英文摘要：
In 2010, Joyce et. al defined the leverage centrality of vertices in a graph as a means to analyze functional connections within the human brain. In this metric a degree of a vertex is compared to the degrees of all it neighbors. We investigate this property from a mathematical perspective. We first outline some of the basic properties and then compute leverage centralities of vertices in different families of graphs. In particular, we show there is a surprising connection between the number of distinct leverage centralities in the Cartesian product of paths and the triangle numbers.
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