  In a network cliques are fully connected subgraphs that reveal which are the
tight communities present in it. Cliques of size c>3 are present in random
Erdos and Renyi graphs only in the limit of diverging average connectivity.
Starting from the finding that real scale free graphs have large cliques, we
study the clique number in uncorrelated scale-free networks finding both upper
and lower bounds. Interesting we find that in scale-free networks large cliques
appear also when the average degree is finite, i.e. even for networks with
power-law degree distribution exponents gamma in the interval (2,3). Moreover
as long as gamma<3 scale-free networks have a maximal clique which diverges
with the system size.
