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Random Graphs and Branching Processes

  • Chapter
Handbook of Large-Scale Random Networks

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 18))

Abstract

During the past decade or so, there has been much interest in generating and analyzing graphs resembling large-scale real-world networks such as the world wide web, neural networks, and social networks. As these large-scale networks seem to be ‘random’, in the sense that they do not have a transparent, well-defined structure, it does not seem too unreasonable to hope to find classical models of random graphs that share their basic properties. Such hopes are quickly dashed, however, since the classical random graphs are all homogeneous, in the sense that all vertices (or indeed all k-sets of vertices) are a priori equivalent in the model. Most real-world networks are not at all like this, as seen most easily from their often unbalanced (power-law) degree sequences. Thus, in order to model such graphs, a host of inhomogeneous random graph models have been constructed and studied.

Research supported in part by NSF grants DMS-0906634, CNS-0721983 and CCF- 0728928, and ARO grant W911NF-06-1-0076.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, UK

    Béla Bollobás

  2. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás

  3. Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK

    Oliver Riordan

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  1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, CB3 0WB, UK

    Béla Bollobás

  2. Dept. Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás  & Robert Kozma  & 

  3. Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Dezső Miklós

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Bollobás, B., Riordan, O. (2008). Random Graphs and Branching Processes. In: Bollobás, B., Kozma, R., Miklós, D. (eds) Handbook of Large-Scale Random Networks. Bolyai Society Mathematical Studies, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69395-6_1

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