Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Lu, Neng-Pin
• Is Part Of: Journal of mathematical sociology. Volume 43:Issue 3(2019)
• Page Start: 164
• Page End: 178
• Publication Date: 2019-07-03
• Subjects: Principal eigenvector -- centrality -- bowtie structure; Sociology -- Periodicals; Sociology -- Mathematical models -- Periodicals; 301.0151
• DOI: 10.1080/0022250X.2018.1555827
• Languages: English
• ISSNs: 0022-250X

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.