Long Paths in Random Apollonian Networks

Long Paths in Random Apollonian Networks

We consider the length L(n) of the longest path in a randomly generated Apollonian Network (ApN) An. We show that w.h.p. L(n) ≤ ne− log c n for any constant c < 2/3.

Parallel Random Apollonian Networks

We 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 scalefree characteristics. To characterize further the structure of P-RAN, we introduce new parameters that we refer to as the parallel degree and the parallel coefficien...

Ramified Random Apollonian Networks

We present a simple algorithm that produces a so called growing Ramified Random Apollonian Networks (R-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 R-RAN, we introduce new parameters that we refer to as the parallel degree and the ramification coefficient, that determine...

Distances in random Apollonian networks

High dimensional random Apollonian networks

We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and clustering coefficients which are determined by the dimension of the network. The values obtained for these parameters are in good agreement with simulation resul...