Numerical evaluation of the upper critical dimension of percolation in scale-free networks
Physical Review E, 75 (6):
066110+ (Juni 2007)DOI: 10.1103/physreve.75.066110
Zusammenfassung
We propose numerical methods to evaluate the upper critical dimension dc of random percolation clusters in Erd\Hos-Rényi networks and in scale-free networks with degree distribution P(k)∼k−λ, where k is the degree of a node and λ is the broadness of the degree distribution. Our results support the theoretical prediction, dc=2(λ−1)∕(λ−3) for scale-free networks with 3<λ<4 and dc=6 for Erd\Hos-Rényi networks and scale-free networks with λ>4. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain dc=6 for all λ>2. Our method also yields a better numerical evaluation of the critical percolation threshold pc for scale-free networks. Our results suggest that the finite size effects increases when λ approaches 3 from above.