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Could any Graph be Turned into a Small-World?

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Distributed Computing (DISC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3724))

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Abstract

In the last decade, effective measurements of real interaction networks have revealed specific unexpected properties. Among these, most of these networks present a very small diameter and a high clustering. Furthermore, very short paths can be effciently found between any pair of nodes without global knowledge of the network (i.e., in a decentralized manner) which is known as the small-world phenomenon [1]. Several models have been proposed to explain this phenomenon [2,3]. However, Kleinberg showed in [4] that these models lack the essential navigability property: in spite of a polylogarithmic diameter, decentralized routing requires the visit of a polynomial number of nodes in these models.

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References

  1. Milgram, S.: The small world problem. Psychology Today 61 (1967)

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  2. Watts, D., Strogatz, S.: Collective dynamics of small-world networks. Nature 393 (1998)

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  3. Newman, M.E.J., Watts, D.J.: Scaling and percolation in the small-world network model. Phys. Rev. 60, 7332–7342 (1999)

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  4. Kleinberg, J.: The small-world phenomenon: an algorithmic perspective. In: Proceedings of the 32nd ACM Symp. on Theory of Computing (STOC), pp. 163–170 (2000)

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  5. Duchon, P., Hanusse, N., Lebhar, E., Schabanel, N.: Could any graph be turned into a small world? To appear in Theoretical Computer Science special issue on Complex Networks (2005); Also available as Research Report LIP-RR2004-62

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Author information

Authors and Affiliations

  1. LABRI, University of Bordeaux, Bordeaux, France

    Philippe Duchon & Nicolas Hanusse

  2. LIP, École Normale Supérieure de Lyon, Lyon, France

    Emmanuelle Lebhar & Nicolas Schabanel

Authors
  1. Philippe Duchon
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  2. Nicolas Hanusse
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  3. Emmanuelle Lebhar
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  4. Nicolas Schabanel
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Editor information

Editors and Affiliations

  1. CNRS and University Paris Diderot,  

    Pierre Fraigniaud

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© 2005 Springer-Verlag Berlin Heidelberg

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Duchon, P., Hanusse, N., Lebhar, E., Schabanel, N. (2005). Could any Graph be Turned into a Small-World?. In: Fraigniaud, P. (eds) Distributed Computing. DISC 2005. Lecture Notes in Computer Science, vol 3724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561927_46

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  • DOI: https://doi.org/10.1007/11561927_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29163-3

  • Online ISBN: 978-3-540-32075-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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