Fractal dimensions of percolating networks

Reuven Cohen and Shlomo Havlin

Physica A: Statistical Mechanics and its Applications, 2004, vol. 336, issue 1, 6-13

Abstract: We use the generating function formalism to calculate the fractal dimensions for the percolating cluster at criticality in Erdős–Rényi (ER) and random scale free (SF) networks, with degree distribution P(k)=ck−λ. We show that the chemical dimension is dl=2 for ER and SF networks with λ>4, as in percolation in d⩾dc=6 dimensions. For 3<λ<4 we show that dl=(λ−2)/(λ−3). The fractal dimension is df=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.

Keywords: Internet; Scale-free; Networks; Fractal; Networks (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:336:y:2004:i:1:p:6-13

DOI: 10.1016/j.physa.2004.01.005

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