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
* Corresponding author
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
2 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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Conference papers
Maria Gradinariu Potop-Butucaru et Hervé Rivano. 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), 2010, Belle Dune, France. pp.TBA, 2010
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Philippe Giabbanelli, Dorian Mazauric, Stéphane Pérennes. Computing the average path length and a label-based routing in a small-world graph. Maria Gradinariu Potop-Butucaru et Hervé Rivano. 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), 2010, Belle Dune, France. pp.TBA, 2010. 〈inria-00472215〉

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