Article contents
Joint Vertex Degrees in the Inhomogeneous Random Graph Model ℊ(n,{pij})
Published online by Cambridge University Press: 04 January 2016
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.
MSC classification
- Type
- General Applied Probability
- Information
- Copyright
- © Applied Probability Trust
References
- 1
- Cited by