Ramified Random Apollonian Networks

Nicolas Bonnel (1) , Pierre-François Marteau (1) , Gildas Ménier (1)

1 VALORIA - Laboratoire de Recherche en Informatique et ses Applications de Vannes et Lorient

We present a simple algorithm that produces a so called Ramified Random Apollonian Networks (R-RAN) in any dimension. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of R-RAN, we introduce new parameters that we refer to as the parallel degree and the ramification coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network. We provide analytical derivations for the computation of the degree and parallel degree distributions, ramification and clustering coefficients and the average path lengths for R-RAN. We finally show that these derivations are in very good agreement with our simulations.

Mots clés: Ramified Random Apollonian Networks growing graph Scale free and small world networks

Domaines: Algorithme et structure de données [cs.DS]

Nicolas Bonnel, Pierre-François Marteau, Gildas Ménier. Ramified Random Apollonian Networks. 2009. ⟨hal-00375016v1⟩