Fractal dimensions of percolating networks

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17 Scopus citations


We use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in Erdos-Rényi (ER) and random scale free (SF) networks, with degree distribution P(k)=ck . We show that the chemical dimension is dl=2 for ER and SF networks with λ>4, as in percolation in d≥d c=6 dimensions. For 3<λ<4 we show that d l=(λ-2)/(λ-3). The fractal dimension is d f=4 (λ>4) and df=2(λ-2)/(λ-3) (3<λ<4), and the embedding dimension is dc=6 (λ>4) and dc=2(λ-1)/(λ-3) (3<λ<4). We discuss the meaning of these dimensions for networks.

Original languageEnglish
Pages (from-to)6-13
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - 1 May 2004
EventProceedings of the XVIII Max Born Symposium at Statistical Physics - Ladek Zdroj, Poland
Duration: 22 Sep 200325 Sep 2003

Bibliographical note

Funding Information:
We thank the Israel Science Foundation for financial support. We thank Daniel ben-Avraham for useful discussion.


  • Fractal
  • Internet
  • Networks
  • Scale-free


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