有向图中基于强连接组件之间的可达性的一种分层的、基于行走的中心性度量

IF 1.3 4区社会学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Sociology Pub Date : 2020-01-12 DOI:10.1080/0022250x.2020.1711753

Neng-pin Lu

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引用次数: 1

摘要

为了测量有向图中的中心性，Bonacich和Lloyd从衰减邻接矩阵的幂级数中总结了一个向量，作为α中心性。然而，alpha中心性的分数通常由拥有邻接矩阵最大特征值的强连接分量中的节点主导。本文基于强连通分量之间的可达性，不仅考虑最大特征值，而且考虑其他较小特征值，对邻接矩阵进行分层衰减;并从层次衰减邻接矩阵的幂级数中得到一个测度。因此，我们提出了分层α中心性，它可以为有向图中具有更高可达性层次的节点产生更高的分数。

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A hierarchical walk-based measure of centrality based on reachability between strongly connected components in a digraph

ABSTRACT For measuring the centrality in a digraph, Bonacich and Lloyd summarized a vector, from the power series of an attenuated adjacency matrix, as the alpha centrality. However, scores of alpha centrality are usually dominated by nodes in the strongly connected component, which owns the largest eigenvalue of the adjacency matrix. In this paper, based on reachability between strongly connected components, we consider not only the largest eigenvalue but also the other smaller ones to attenuate the adjacency matrix hierarchically; and obtain a measure from the power series of the hierarchically attenuated adjacency matrix. Consequently, we propose the hierarchical alpha centrality, which can yield higher scores for nodes at higher hierarchies of reachability in a digraph.

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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.