Parallel Random Apollonian Networks

The authors present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of P-RAN, they introduce new parameters that they refer to as the parallel degree and the parallel coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network. They provide analytical derivations for the computation of the degree and parallel degree distributions, parallel and clustering coefficients.