is found for $\rho=0.5$. An example of this for $k=6$ is shown in Fig. \[k6c\] where the initial fraction of cooperators was $\rho_c=0.1$ (compare Figs. \[k6b\] and \[k6c\]).

When, instead, the fraction of realizations that converge is considered, the picture that emerges is rather different, as Figs. \[k8d\] and  \[k6c\] show. In this case, ordered networks are less favourable for the preservation (and eventual expansion) of cooperation than completely random networks. As before, the behaviour between these two extremes is not monotonic. A feature of these curves that stands out is that, for the same values of $C$, they seem to depend very weakly on the type of substrate used to generate them.

![ Steady cooperator density $\rho_c$ as a function of the clustering coefficient $C$, for $K=6$ and $\rho_c(0)=0.1$. (l) and (r) in the caption refer to lattice and ring networks respectively. Only those realizations that showed to the survival of cooperators were considered. []{data-label="k6b"}](imik6b.eps)

![ Fraction of realizations that converge to a steady state with a positive number of cooperators, for networks with $k=8$. []{data-label="k8d"}](imik8b.eps)

The difference of the evolutionary dynamics of populations starting from many, or few, cooperators can be shown even more clearly using the same 