Growing Networks Through Random Walks Without Restarts

  • Bernardo Amorim
  • Daniel Figueiredo
  • Giulio Iacobelli
  • Giovanni Neglia
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 644)

Abstract

Networkgrowthandevolution is a fundamental theme that has puzzled scientists for the past decades. A number of models have been proposed to capture important properties of real networks. In an attempt to better describe reality, more recent growth models embody local rules of attachment, however they still require a primitive to randomly select an existing network node and then some kind of global knowledge about the network (at least the set of nodes and how to reach them). We propose a purely local network growth model that makes no use of global sampling across the nodes. The model is based on a continuously moving random walk that after s steps connects a new node to its current location, but never restarts. Through extensive simulations and theoretical arguments, we analyze the behavior of the model finding a fundamental dependency on the parity of s, where networks with either exponential or a conditional power law degree distribution can emerge. As s increases parity dependency diminishes and the model recovers the degree distribution of Barabási-Albert preferential attachment model. The proposed purely local model indicates that networks can grow to exhibit interesting properties even in the absence of any global rule, such as global node sampling.

References

  1. 1.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Blanchard, P., Krueger, T., Ruschhaupt, A.: Small world graphs by iterated local edge formation. Phys. Rev. E 71, 046139 (2005)Google Scholar
  3. 3.
    Cannings, C., Jordan, J.: Random walk attachment graphs. Electron. Commun. Probab. 18, 1–5 (2013)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Colman, E.R., Rodgers, G.J.: Local rewiring rules for evolving complex networks. Phys. A: Stat. Mech. Appl. 416, 80–89 (2014)CrossRefGoogle Scholar
  5. 5.
    Gabel, A., Redner, S.: Sublinear but never superlinear preferential attachment by local network growth. J. Stat. Mech.: Theory Exp. 2013(02), P02043 (2013)Google Scholar
  6. 6.
    Ikeda, N.: Network formation determined by the diffusion process of random walkers. J. Phys. A: Math. Theor. 41(23), 235005 (2008)Google Scholar
  7. 7.
    Ikeda, N.: Network formed by movements of random walkers on a bethe lattice. In: Journal of Physics: Conference Series, vol. 490, p. 012189. IOP Publishing (2014)Google Scholar
  8. 8.
    Li, M., Gao, L., Fan, Y., Wu, J., Di, Z.: Emergence of global preferential attachment from local interaction. New J. Phys. 12(4), 043029 (2010)Google Scholar
  9. 9.
    Saramäki, J., Kaski, K.: Scale-free networks generated by random walkers. Phys. A: Stat. Mech. Appl. 341, 80–86 (2004)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Vázquez, A.: Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations. Phys. Rev. E 67(5), 056104 (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Bernardo Amorim
    • 1
  • Daniel Figueiredo
    • 1
  • Giulio Iacobelli
    • 1
  • Giovanni Neglia
    • 2
  1. 1.Department of Computer and System Engineering (PESC)Federal University of Rio de Janeiro (UFRJ)Rio de JaneiroBrazil
  2. 2.MAESTRO Team, INRIASophia-AntipolisFrance

Personalised recommendations