Generating-function approach for bond percolation in hierarchical networks

Takehisa Hasegawa, Masataka Sato, Koji Nemoto

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22 Citations (Scopus)


We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts p and that of the ordinary bonds p. The system has a critical phase in which the percolating probability P takes an intermediate value 0<P<1. Using generating function approach, we calculate the fractal exponent ψ of the root clusters to show that ψ varies continuously with p in the critical phase. We confirm numerically that the distribution ns of cluster size s in the critical phase obeys a power law ns s-τ, where τ satisfies the scaling relation τ=1+ ψ-1. In addition the critical exponent β (p) of the order parameter varies as p, from β 0.164694 at p=0 to infinity at p= pc =5/32.

Original languageEnglish
Article number046101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - 2010 Oct 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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