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A Spatial Preferential Attachment Model with Local Clustering

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Algorithms and Models for the Web Graph (WAW 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8305))

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Abstract

A class of growing networks is introduced in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favouring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Most notably, empirical degree distributions converge to a limit law, which can be a power law with any exponent τ > 2, and the average clustering coefficient converges to a positive limit. Our main tool to show these and other results is a weak law of large numbers in the spirit of Penrose and Yukich, which can be applied thanks to a novel rescaling idea. We also conjecture that the networks have a robust giant component if τ is sufficiently small.

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Author information

Authors and Affiliations

  1. École Normale Supérieure de Lyon, France

    Emmanuel Jacob

  2. University of Bath, UK

    Peter Mörters

Authors
  1. Emmanuel Jacob
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  2. Peter Mörters
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Ryerson University, Toronto, ON, Canada

    Anthony Bonato  & Paweł Prałat  & 

  2. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Michael Mitzenmacher

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Jacob, E., Mörters, P. (2013). A Spatial Preferential Attachment Model with Local Clustering. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2013. Lecture Notes in Computer Science, vol 8305. Springer, Cham. https://doi.org/10.1007/978-3-319-03536-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-03536-9_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03535-2

  • Online ISBN: 978-3-319-03536-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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