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The phase transition in inhomogeneous random graphs (2005)
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| Citations: | 179 - 29 self |
BibTeX
@MISC{Bollobás05thephase,
author = {Bela Bollobás and Svante Janson and Oliver Riordan},
title = {The phase transition in inhomogeneous random graphs},
year = {2005}
}
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Abstract
The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, power-law degree distributions. Thus there has been a lot of recent interest in defining and studying ‘inhomogeneous ’ random graph models. One of the most studied properties of these new models is their ‘robustness’, or, equivalently, the ‘phase transition ’ as an edge density parameter is varied. For G(n, p), p = c/n, the phase transition at c = 1 has been a central topic in the study of random graphs for well over 40 years. Many of the new inhomogenous models are rather complicated; although there are exceptions, in most cases precise questions such as determining exactly the critical point of the phase transition are approachable only when there is independence between the edges. Fortunately, some models studied have this already, and others can be approximated by models with
Keyphrases
phase transition inhomogeneous random graph org ab math random graph many graph edge density parameter classical random graph model recent interest power-law degree distribution new inhomogenous model inhomogeneous random graph model critical point new model real world central topic typical value studied property
