  We introduce a community network model which exhibits scale-free property and
study the evolutionary Prisoner's Dilemma game (PDG) on this network model. It
is found that the frequency of cooperators decreases with the increment of the
average degree $\bar{k}$ from the simulation results. And reducing
inter-community links can promote cooperation when we keep the total links
(including inner-community and inter-community links) unchanged. It is also
shown that the heterogeneity of networks does not always enhance cooperation
and the pattern of links among all the vertices under a given
degree-distribution plays a crucial role in the dominance of cooperation in the
network model.

Physics and Society