A deterministic small-world network created by edge iterations

Abstract

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.

9 pages, 1 figure. to appear in Physica A

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• 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
• Farey Graphs as Models for Complex Networks
• Trapping in scale-free networks with hierarchical organization of modularity
• Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
• Random walks in modular scale-free networks with multiple traps
• Local-world evolving networks with tunable clustering
• Correlations in random Apollonian network
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks
• Recursive weighted treelike networks
• Deterministic weighted scale-free small-world networks
• A geometric growth model interpolating between regular and small-world networks
• From regular to growing small-world networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Constructions and properties of a class of random scale-free networks
• Vertex labeling and routing in expanded Apollonian networks
• Deterministic scale-free networks created in a recursive manner