In this article, we investigate several issues related to the use of the index S(G), known as the Zagreb index (see Gutman and Das, 2004) or “S-metric” (Alderson and Li, 2007). We present some new upper and lower bounds for S(G), in terms of the degree sequence of G. Then, we concentrate on trees and prove that in trees with maximum S(G) the eigenvector ordering is coherent with the degree ordering; that is, degree central vertices are also eigenvector central. This confirms results given in Bonacich (2007). Further, we show that these trees have minimum diameter and maximum spectral radius in the set of trees with a given degree sequence. A simple application to a company organizational network is provided.

Torriero, A., Stefani, S., Grassi, R., Extremal properties of graphs and eigencentrality in trees with a given degree sequence, <<THE JOURNAL OF MATHEMATICAL SOCIOLOGY>>, 2010; 34 (2): 115-135. [doi:10.1080/00222500903221563] [http://hdl.handle.net/10807/14023]

Extremal properties of graphs and eigencentrality in trees with a given degree sequence

Torriero;Anna; Stefani;Silvana; Grassi
2010

Abstract

In this article, we investigate several issues related to the use of the index S(G), known as the Zagreb index (see Gutman and Das, 2004) or “S-metric” (Alderson and Li, 2007). We present some new upper and lower bounds for S(G), in terms of the degree sequence of G. Then, we concentrate on trees and prove that in trees with maximum S(G) the eigenvector ordering is coherent with the degree ordering; that is, degree central vertices are also eigenvector central. This confirms results given in Bonacich (2007). Further, we show that these trees have minimum diameter and maximum spectral radius in the set of trees with a given degree sequence. A simple application to a company organizational network is provided.
Inglese
Torriero, A., Stefani, S., Grassi, R., Extremal properties of graphs and eigencentrality in trees with a given degree sequence, <<THE JOURNAL OF MATHEMATICAL SOCIOLOGY>>, 2010; 34 (2): 115-135. [doi:10.1080/00222500903221563] [http://hdl.handle.net/10807/14023]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/14023
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