TY - JOUR

T1 - Aggregating nonnegative eigenvectors of the adjacency matrix as a measure of centrality for a directed graph

AU - Lu, Neng Pin

N1 - Publisher Copyright:
© 2017 Taylor & Francis.

PY - 2017

Y1 - 2017

N2 - Eigenvector centrality is a popular measure that uses the principal eigenvector of the adjacency matrix to distinguish importance of nodes in a graph. To find the principal eigenvector, the power method iterating from a random initial vector is often adopted. In this article, we consider the adjacency matrix of a directed graph and choose suitable initial vectors according to strongly connected components of the graph instead so that nonnegative eigenvectors, including the principal one, can be found. Consequently, for aggregating nonnegative eigenvectors, we propose a weighted measure of centrality, called the aggregated-eigenvector centrality. Weighting each nonnegative eigenvector by the reachability of the associated strongly connected component, we can obtain a measure that follows a status hierarchy in a directed graph.

AB - Eigenvector centrality is a popular measure that uses the principal eigenvector of the adjacency matrix to distinguish importance of nodes in a graph. To find the principal eigenvector, the power method iterating from a random initial vector is often adopted. In this article, we consider the adjacency matrix of a directed graph and choose suitable initial vectors according to strongly connected components of the graph instead so that nonnegative eigenvectors, including the principal one, can be found. Consequently, for aggregating nonnegative eigenvectors, we propose a weighted measure of centrality, called the aggregated-eigenvector centrality. Weighting each nonnegative eigenvector by the reachability of the associated strongly connected component, we can obtain a measure that follows a status hierarchy in a directed graph.

KW - Nonnegative eigenvector

KW - Power method

KW - Strongly connected component

UR - http://www.scopus.com/inward/record.url?scp=85020282867&partnerID=8YFLogxK

U2 - 10.1080/0022250X.2017.1328680

DO - 10.1080/0022250X.2017.1328680

M3 - 文章

AN - SCOPUS:85020282867

SN - 0022-250X

VL - 41

SP - 139

EP - 154

JO - Journal of Mathematical Sociology

JF - Journal of Mathematical Sociology

IS - 3

ER -