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March 2012 Joint vertex degrees in the inhomogeneous random graph model G(n, {pij})
Kaisheng Lin, Gesine Reinert
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Adv. in Appl. Probab. 44(1): 139-165 (March 2012). DOI: 10.1239/aap/1331216648

Abstract

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly inhomogeneous distribution, only when the degrees are large can we reasonably approximate the joint counts as independent. The proofs are based on Stein's method and the Stein-Chen method with a new size-biased coupling for such inhomogeneous random graphs, and, hence, bounds on the distributional distance are obtained. Finally, we illustrate that apparent (pseudo-)power-law-type behaviour can arise in such inhomogeneous networks despite not actually following a power-law degree distribution.

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Kaisheng Lin. Gesine Reinert. "Joint vertex degrees in the inhomogeneous random graph model G(n, {pij})." Adv. in Appl. Probab. 44 (1) 139 - 165, March 2012. https://doi.org/10.1239/aap/1331216648

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

MathSciNet: MR2951550
Digital Object Identifier: 10.1239/aap/1331216648

Subjects:
Primary: 60F05
Secondary: 05C80, 90B15

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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