High Dimensional Apollonian Networks

Abstract

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.

References in corpus (6)

• Maximal planar networks with large clustering coefficient and power-law degree distribution
• Self-similar disk packings as model spatial scale-free networks
• Recursive graphs with small-world scale-free properties
• Magnetic models on Apollonian networks
• Statistics of Cycles: How Loopy is your Network?
• Exactly solvable scale-free network model

Cited by in corpus (30)

• Network geometry with flavor: from complexity to quantum geometry
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Weighted Growing Simplicial Complexes
• Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation
• Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
• Synchronization in Network Geometries with Finite Spectral Dimension
• Evolving Apollonian Networks with Small-world Scale-free topologies
• A general geometric growth model for pseudofractal scale-free web
• Exact analytical solution of average path length for Apollonian networks
• Random walks on the Apollonian network with a single trap
• Evolving small-world scale-free networks consist of cliques
• Evolving small-world networks with geographical attachment preference
• Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
• Dimensionality of social networks using motifs and eigenvalues
• Local-world evolving networks with tunable clustering
• Correlations in random Apollonian network
• Deterministic hierarchical networks
• Recursive weighted treelike networks
• A geometric growth model interpolating between regular and small-world networks
• Planar unclustered scale-free graphs as models for technological and biological networks
• Estimate for the fractal dimension of the Apollonian gasket in d dimensions
• Contact graphs of disk packings as a model of spatial planar networks
• Constructions and properties of a class of random scale-free networks
• Vertex labeling and routing in expanded Apollonian networks
• Diophantine Networks
• Transfinite fractal dimension of trees and hierarchical scale-free graphs
• Deterministic scale-free networks created in a recursive manner
• Binary Apollonian networks
• Degrees and distances in random and evolving Apollonian networks
• Nearest-neighbour directed random hyperbolic graphs