论文标题
一些图家族的谐波集中化
Harmonic Centralization of Some Graph Families
论文作者
论文摘要
中心性描述了图中节点的重要性，并以各种度量进行建模。它的全局类似物称为集中化，是基于节点级中心度度量计算图形级中心性评分的一般公式。后者使我们能够根据给定网络的连接集中在单个顶点或一组顶点的程度上比较图。社交网络分析中中心性的衡量标准之一是和声中心性。如果没有一个节点到另一个节点没有路径，则每个节点与其他节点的测量距离的倒数总和，而总和通过将其除以$ M-1 $将其归一化，其中$ m $是图形的节点的数量。在本文中，我们提供了一些关于一些重要图系列的谐波集中化的结果，希望当人们确定更复杂图的谐波集中化时，本文生成的公式将被使用。
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality measure. The latter enables us to compare graphs based on the extent to which the connections of a given network are concentrated on a single vertex or group of vertices. One of the measures of centrality in social network analysis is harmonic centrality. It sums the inverse of the geodesic distances of each node to other nodes where it is 0 if there is no path from one node to another, with the sum normalized by dividing it by $m-1$, where $m$ is the number of nodes of the graph. In this paper, we present some results regarding the harmonic centralization of some important families of graphs with the hope that formulas generated herein will be of use when one determines the harmonic centralization of more complex graphs.
