Vertex labeling and routing in expanded Apollonian networks

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their nodes that allows one to determine a shortest path routing between any two nodes of the network based only on the labels. PACS numbers: 02.10.Ox, 89.20.Ff, 89.75.D...

. so c - ph ] 3 1 O ct 2 00 6 Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.

High dimensional Apollonian networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension. PACS numbers: 89.75.Hc, 89.75.Da, 89.20.Hh High dimensional Apollonian networks 2

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...

Distances in random Apollonian networks