and now the most favorable networks in terms of cooperation are completely random ones. There are even some values of $t$ for which the dependence with $C$ is not monotonic.

![ Average value of the steady-state fraction of cooperators for a stochastic evolutionary dynamics, for several values of $t$ for random ring networks with $k=8$, and for $\rho_c(0)=0.5$ (panel A) and $\rho_c(0)=0.1$ (panel B).[]{data-label="figstoch"}](stoch.eps)

![ Fraction of realizations that converge to a steady state with a positive number of cooperators, for networks with $k=6$. []{data-label="k6c"}](imik6c.eps)

So far we have shown that the clustering coefficient of the networks has an important influence on the steady state. But whether or not this influence is beneficial depends strongly on the initial fraction of cooperators, both for deterministic and stochastic evolutionary dynamics. The possible causes for this are addressed in the next section.

Role of the initial fraction of cooperators
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To understand the conflicting ways in which network clustering can affect cooperation we study in some detail the deterministic dynamics, and hope that some conclusions apply also to the stochastic case. Furthermore, in terms of the range of possible clustering coefficients we limit ourselves to analyze what happens for networks at the two 