Aggregating nonnegative eigenvectors of the adjacency matrix as a measure of centrality for a directed graph
| Autor: | Neng-Pin Lu |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Strongly connected component 050402 sociology Algebra and Number Theory Degree matrix Sociology and Political Science Spectral graph theory 05 social sciences MathematicsofComputing_GENERAL MathematicsofComputing_NUMERICALANALYSIS 050401 social sciences methods Directed graph Combinatorics Graph energy 0504 sociology Adjacency list Regular graph Adjacency matrix Social Sciences (miscellaneous) MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | The Journal of Mathematical Sociology. 41:139-154 |
| ISSN: | 1545-5874 0022-250X |
| DOI: | 10.1080/0022250x.2017.1328680 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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