Eigenvector centrality and uniform dominant eigenvalue of graph components

Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be used. Two cases are considered; first where the a single component in the graph has the dominant eigenvalue, secondly when there are at least two components that share the dominant eigenvalue for the graph. In the first case we implement and compare the method to the usual approach (power method) for calculating eigenvector centrality while in the second case with shared dominant eigenvalues we show some theoretical and numerical results. Keywords: Eigenvector centrality, power iteration, graph, strongly connected component.

Keywords

Graph Components, Eigenvector Centrality, Uniform Dominant Eigenvalue

Citation

Anguzu, C., Engström, C., Mango, J. M., Kasumba, H., Silvestrov, S., & Abola, B. (2021). Eigenvector Centrality and Uniform Dominant Eigenvalue of Graph Components. arXiv preprint arXiv:2107.09137.https://doi.org/10.48550/arXiv.2107.09137

URI

https://nru.uncst.go.ug/handle/123456789/8847

Collections

Natural Sciences

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