We propose a numerical method to evaluate the upper critical dimension dc
of random percolation clusters in Erd\H{o}s-R\'{e}nyi 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 report the theoretical prediction, dc=2(λ−1)/(λ−3) for scale-free networks with 3<λ<4 and dc=6
for Erd\H{o}s-R\'{e}nyi 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.Comment: 10 pages, 5 figure