generated with the following algorithm. Starting from an ordered network (defined below) we select at random two pairs of connected nodes. Then we ‘cut’ both connections and connect each individual to one of the individuals it had not been connected before. In other words, the connections are swapped. If this change gives a network with larger $C$, it is accepted and the network is updated. If it does not increase $C$, the change is only accepted with a fixed (and typically small) probability. This process goes on until the clustering coefficient has reached the desired value. Notice that this procedure leaves the degree distribution of the original network unchanged. When the desired clustering coefficient is very low, it is to be expected that the resulting networks is very close to a regular random network, independently of the starting one. On the other hand, for larger values of $C$ it is to be expected that the effect of the starting network is much larger. For this reason we use two different starting networks: ring networks where each node is connected symmetrically to the closest $k$ nodes, and 2-dimensional lattice networks. The networks generated from these two classes are called, respectively, random 