Limit distributions for the diameter and the shortest path hopcount in random graphs with positive integer edge costs

摘要

The probability distribution of the diameter of a network modelconsisting of a complete digraph with positive integer random edge costsis considered. Edge costs are chosen independently for each node pairaccording to common probability distributions for each edge direction.Bounds and some sharp limit results for the diameter distribution in thelimit as the number of nodes tends to infinity are derived. In addition,limit bounds are determined for the distribution of the number of hopsin a shortest path between two arbitrary nodes in the graph. Numericalexamples are presented to illustrate these results