PATHS IN THE SIMPLE RANDOM GRAPH AND THE WAXMAN GRAPH

  • Authors:
  • Piet Van Mieghem

  • Affiliations:
  • Information Technology and Systems, Delft University of Technology, Delft, The Netherlands, E-mail: P.VanMieghem@its.tudelft.nl

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2001

Quantified Score

Hi-index 0.00

Visualization

Abstract

The Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. For the Waxman graphs, we present analytic, exact expressions for the link density (average number of links) and the average number of paths between two nodes. These results show the similarity of Waxman graphs to the simpler class Gp(N). The first result enables one to compare simulations performed on the Waxman graph with those on other graphs with same link density. The average number of paths in Waxman graphs can be useful to dimension (or estimate) routing paths in networks. Although higher-order moments of the number of paths in Gp(N) are difficult to compute analytically, the probability distribution of the hopcount of a path between two arbitrary nodes seems well approximated by a Poisson law.