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The Phase Transition and Connectedness in Uniformly Grown Random Graphs

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Algorithms and Models for the Web-Graph (WAW 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3243))

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Abstract

We consider several families of random graphs that grow in time by the addition of vertices and edges in some ‘uniform’ manner. These families are natural starting points for modelling real-world networks that grow in time. Recently, it has been shown (heuristically and rigorously) that such models undergo an ‘infinite-order phase transition’: as the density parameter increases above a certain critical value, a ‘giant component’ emerges, but the speed of this emergence is extremely slow. In this paper we shall present some of these results and investigate the connection between the existence of a giant component and the connectedness of the final infinite graph.

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Author information

Authors and Affiliations

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

    Béla Bollobás

  2. Trinity College, Cambridge, CB2 1TQ, UK

    Béla Bollobás & Oliver Riordan

  3. Royal Society Research Fellow, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK

    Oliver Riordan

Authors
  1. Béla Bollobás
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  2. Oliver Riordan
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Editor information

Editors and Affiliations

  1. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

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© 2004 Springer-Verlag Berlin Heidelberg

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Bollobás, B., Riordan, O. (2004). The Phase Transition and Connectedness in Uniformly Grown Random Graphs. In: Leonardi, S. (eds) Algorithms and Models for the Web-Graph. WAW 2004. Lecture Notes in Computer Science, vol 3243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30216-2_1

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  • DOI: https://doi.org/10.1007/978-3-540-30216-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23427-2

  • Online ISBN: 978-3-540-30216-2

  • eBook Packages: Springer Book Archive

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