Algebraic Connectivity for Vertex-Deleted Subgraphs, and a Notion of Vertex Centrality

Kirkland, Steve (2010) Algebraic Connectivity for Vertex-Deleted Subgraphs, and a Notion of Vertex Centrality. Discrete Mathematics, 310 (4). pp. 911-921. ISSN 0012-365X

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Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G\v. Denote the algebraic connectivities of G and G\v by α(G) and (G\v), respectively. In this paper, we consider the functions ∅(v) = α(G)− α(G\v) and k(v) = α(G\v)/α(G), provide attainable upper and lower bounds on both functions, and characterise the equality cases in those bounds. The function yields a measure of vertex centrality, and we apply that measure to analyse certain graphs arising from food webs.

Item Type: Article
Keywords: Algebraic connectivity; Vertex-deleted subgraph; Vertex centrality; Hamilton Institute.
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1894
Identification Number: 10.1016/j.disc.2009.10.011
Depositing User: Hamilton Editor
Date Deposited: 23 Mar 2010 10:06
Journal or Publication Title: Discrete Mathematics
Publisher: Elsevier BV, North-Holland
Refereed: Yes

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