Aggregating nonnegative eigenvectors of the adjacency matrix as a measure of centrality for a directed graph. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Lu, Neng-Pin
• Is Part Of: Journal of mathematical sociology. Volume 41:Issue 3(2017)
• Page Start: 139
• Page End: 154
• Publication Date: 2017-07-03
• Subjects: Nonnegative eigenvector -- power method -- strongly connected component; Sociology -- Periodicals; Sociology -- Mathematical models -- Periodicals; 301.0151
• DOI: 10.1080/0022250X.2017.1328680
• Languages: English
• ISSNs: 0022-250X

Abstract

ABSTRACT: 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.