Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph
Bibliographic Data
| ID | 10142433 |
|---|---|
| Authors | Neng‐Pin Lu (0000-0002-4310-4171, Chang Gung University, corresponding author), Neng-Pin Lu (Chang Gung University) |
| Year | 2018 |
| Volume | 43 |
| Issue | 3 |
| Pages | 164-178 |
| Publication date | 2018-12-17 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Mathematical Sociology (JOURNAL) |
| Journal identifiers | ISSN: 0022-250X • E-ISSN: 1545-5874 |
| Publisher | Taylor & Francis (PUBLISHER • GB) |
| DOI | 10.1080/0022250x.2018.1555827 |
| OpenAlex | W2904510983 |
| Language | EN |
| Citations received | 2 |
| References cited | 24 |
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
Adjacency list · Adjacency matrix · Centrality · Combinatorics · Diagonal · Diagonal matrix · Digraph · Discrete mathematics · Eigenvalues and eigenvectors · Geometry · Graph · Graph energy · Graph power · Line graph · Physics · Principal (computer security · Principal component analysis · Strongly connected component · Complex Network Analysis Techniques · Computer Science · Graph theory and applications · Mathematics · Opinion Dynamics and Social Influence
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| Citations per year | 0.33 |
|---|---|
| Citation span | 2020 - 2021 (2) |
| Highly cited | No |