Impact of single links in competitive percolation View Full Text


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Article Info

DATE

2011-01-16

AUTHORS

Jan Nagler, Anna Levina, Marc Timme

ABSTRACT

How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of ‘explosive percolation’ suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single-link additions. We show that in generic competitive percolation processes, including those showing explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce substantial gaps, because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively. More... »

PAGES

265-270

References to SciGraph publications

  • 1999. Percolation in NONE
  • 2007-09. Birth control for giants in COMBINATORICA
  • 2006-04-01. Origins of fractality in the growth of complex networks in NATURE PHYSICS
  • 2001-03. Exploring complex networks in NATURE
  • 2010-05-19. Explosive percolation in the human protein homology network in THE EUROPEAN PHYSICAL JOURNAL B
  • 2009-09. Structure comes to random graphs in NATURE PHYSICS
  • 1996. Fractals and Disordered Systems in NONE
  • 2010-04. Catastrophic cascade of failures in interdependent networks in NATURE
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    http://scigraph.springernature.com/pub.10.1038/nphys1860

    DOI

    http://dx.doi.org/10.1038/nphys1860

    DIMENSIONS

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