Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph

IF 1.3 4区社会学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Sociology Pub Date : 2018-12-17 DOI:10.1080/0022250X.2018.1555827

Neng-pin Lu

引用次数: 2

Abstract

ABSTRACT Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.

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利用邻接矩阵的主特征向量加上对角权值组成有向图的中心性测度并识别有向图的领结结构

摘要邻接矩阵的主特征向量常被用作图或有向图的中心性度量。然而，以往对有向图的类主特征向量度量通常只考虑邻接子矩阵具有最大特征值的强连通分量。本文对有向图中的每一个强连通分量，在邻接矩阵中对其成员节点的对角线元素增加权值，使修改后的矩阵具有新的唯一的最大特征值和相应的主特征向量。因此，我们使用基于不同强连接分量的改进矩阵的新主特征向量，不仅可以组成中心性度量，而且可以识别有向图的蝴蝶结结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Sociology 数学-数学跨学科应用

CiteScore

2.90

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The goal of the Journal of Mathematical Sociology is to publish models and mathematical techniques that would likely be useful to professional sociologists. The Journal also welcomes papers of mutual interest to social scientists and other social and behavioral scientists, as well as papers by non-social scientists that may encourage fruitful connections between sociology and other disciplines. Reviews of new or developing areas of mathematics and mathematical modeling that may have significant applications in sociology will also be considered. The Journal of Mathematical Sociology is published in association with the International Network for Social Network Analysis, the Japanese Association for Mathematical Sociology, the Mathematical Sociology Section of the American Sociological Association, and the Methodology Section of the American Sociological Association.