Numbers of n-th Neighbors and Node-To-Node Distances in Growing Networks

Topology of exponential and scale-free trees and simple graphs is investigated numerically. The numbers of the nearest neighbors, the next-nearest neighbors, the next-next-nearest neighbors, the 4-th and the 5-th neighbors are calculated. The functional dependence [A.E. Motter, T. Hishikawa, Y.-Ch. Lai, Phys. Rev. E66, 065103(R) (2002)] of the node-to-node distance dij on the product of connectivities kikj has been studied numerically. The results of simulations for exponential networks agree with the existing analytical predictions. (author)