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 -