disorder. Notice that the curves only overlap for very small values of the clustering coefficient. This means that a large amount of disorder is needed for the network to ‘forget’ the starting substrate.

![Steady cooperator density $\rho_c$ as a function of the clustering coefficient $C$, for $K=8$ and $\rho_c(0)=0.5$. (l) and (r) in the caption refer to lattice and ring networks respectively.[]{data-label="k8"}](imik8.eps)

In Fig. \[k4\] only one point is shown for random lattice networks because both the square lattice and the completely random network with $k=4$ have a vanishing clustering coefficient. The large difference seen in Fig. \[k4\] between the steady state fraction of cooperators could be attributed to the much shorter minimal distances between nodes in random regular networks (which have a diameter $\approx \log N$ [@bollo]) or to the presence of short loops in the square lattice (see next section).

When the initial state has less collaborators, the situation is more complex to analyze because for some systems the population evolves to an equilibrium state where all the cooperators have been eliminated. If, however, we consider only those systems that have a steady state with a non vanishing fraction of cooperators, the picture is very similar to what 