  In the last years the Prisoner Dilemma (PD) has become a paradigm for the
study of the emergence of cooperation in spatially structured populations. Such
structure is usually assumed to be given by a graph. In general, the success of
cooperative strategies is associated with the possibility of forming globular
clusters, which in turn depends on a feature of the network that is measured by
its clustering coefficient. In this work we test the dependence of the success
of cooperation with the clustering coefficient of the network, for several
different families of networks. We have found that this dependence is far from
trivial. Additionally, for both stochastic and deterministic dynamics we have
also found that there is a strong dependence on the initial composition of the
population. This hints at the existence of several different mechanisms that
could promote or hinder cluster expansion. We have studied in detail some of
these mechanisms by concentrating on completely ordered networks (large
clustering coefficient) or completely random networks (vanishing clustering
coefficient).
