Remarks on Distance Distributions for Graphs Modeling Computer Networks

The Wiener polynomial of a graph G is a generating function for the distance distribution dd(G) = (D1, D2,…,Dt), where Di is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G. We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of graphs that model certain large classes of computer networks. These provide a straightforward means of computing distance and timing statistics when designing new networks or enlarging existing networks.