Computing the average path length and a label-based routing in a small-world graph

Philippe Giabbanelli (1) , Dorian Mazauric (1, 2) , Stéphane Pérennes (1)

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
2 MAESTRO - Models for the performance analysis and the control of networks

We study two characteristics of a small-world graph proposed by Zhang et al. to model complex networks. Our study relies on the recursive structure of the graph. Firstly, we use it to design a labelling scheme in order to create an implicit routing (i.e., a routing scheme based on the label of vertices). Secondly, proving the average distance in this graph was arduous, thus Zhang et al. chose to study the diameter: we establish a closed-form formula of the average distance, proved using the recursive structure. Thus, we characterize that the graph is small-world and not ultra small-world as was still possible. Our proof is of particular interest for other graphs based on similar recursive structures.

Keywords: Recursive graph; Labeling scheme; Decentralized routing

Domains: Networking and Internet Architecture [cs.NI]

Philippe Giabbanelli, Dorian Mazauric, Stéphane Pérennes. Computing the average path length and a label-based routing in a small-world graph. 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), 2010, Belle Dune, France. pp.TBA. ⟨inria-00472215⟩