Distance distribution and reliability of small-world networks

We have studied the distribution of distances in small-world networks by co mputer simulation. We found that in a small-world network, the longest dist ance between two vertices is just slightly longer than the average distance , indicating that the efficiency of the network is absolute rather than in average. We also investigated the robustness of a small-world network by ra ndomly cutting some long paths in the network. The results show that the ne twork is reliable against random cutting.