NUMBERS OF n-TH NEIGHBORS AND NODE-TO-NODE DISTANCES IN GROWING NETWORKS

摘要

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 d_(ij) on the product of connectivities k_ik_j has been studied numerically. The results of simulations for exponential networks agree with the existing analytical predictions.