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Robustness of Spatial Preferential Attachment Networks

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Algorithms and Models for the Web Graph (WAW 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9479))

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Abstract

We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering one can independently tune the power law exponent \(\tau >2\) of the degree distribution and a parameter \(\delta >1\) determining the decay rate of the probability of long edges. We argue that the network is robust if \(\tau <2+\frac{1}{\delta }\), but fails to be robust if \(\tau >2+\frac{1}{\delta -1}\). Hence robustness depends not only on the power-law exponent but also on the clustering features of the network.

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Acknowledgements

We gratefully acknowledge support of this project by the European Science Foundation through the research network Random Geometry of Large Interacting Systems and Statistical Physics (RGLIS), and by CNRS. A full version of this paper has been submitted for publication elsewhere [18].

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Authors and Affiliations

  1. École Normale Supérieure de Lyon, Lyon, France

    Emmanuel Jacob

  2. University of Bath, Bath, UK

    Peter Mörters

Authors
  1. Emmanuel Jacob
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  2. Peter Mörters
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Correspondence to Peter Mörters .

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Editors and Affiliations

  1. Purdue University, West Lafayette, Indiana, USA

    David F. Gleich

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Júlia Komjáthy

  3. University of Twente, Enschede, The Netherlands

    Nelly Litvak

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Jacob, E., Mörters, P. (2015). Robustness of Spatial Preferential Attachment Networks. In: Gleich, D., Komjáthy, J., Litvak, N. (eds) Algorithms and Models for the Web Graph. WAW 2015. Lecture Notes in Computer Science(), vol 9479. Springer, Cham. https://doi.org/10.1007/978-3-319-26784-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-26784-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26783-8

  • Online ISBN: 978-3-319-26784-5

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