The effect of a change in p is extremely nonlinear as is visually demonstrated by the difference between Figs. 2 Effect of disorder on the distance between vertices of the network. Black indicates that a link is present between the two vertices while green indicates the absence of a link. Note that we apply periodic boundary conditions, that is, vertex 1 follows vertex n . We use the relief of the surface and a color scheme to represent the distance between two vertices.
Greater height indicates larger distance.
For the regular network, the contour lines are parallel to the diagonal. To investigate this question, we need to look at the behavior of the system as a function of p for different values of n . This result relies on the fact that the crossover from large to small worlds is obtained with only a small but finite fraction of rewired links. We find that the above scaling ansatz is indeed verified by the average distance l between any two vertices of the network. Scale-free networks emerge in the context of a growing network in which new vertices connect preferentially to the more highly connected vertices in the network.