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 -λ. 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.
|Number of pages||8|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - 1 May 2004|
|Event||Proceedings of the XVIII Max Born Symposium at Statistical Physics - Ladek Zdroj, Poland|
Duration: 22 Sep 2003 → 25 Sep 2003
Bibliographical noteFunding Information:
We thank the Israel Science Foundation for financial support. We thank Daniel ben-Avraham for useful discussion.