A geometric growth model interpolating between regular and small-world networks

Abstract

We propose a geometric growth model which interpolates between one-dimensional linear graphs and small-world networks. The model undergoes a transition from large to small worlds. We study the topological characteristics by both theoretical predictions and numerical simulations, which are in good accordance with each other. Our geometrically growing model is a complementarity for the static WS model.

10 pages, 6 figures

References in corpus (27)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Hierarchical organization of modularity in metabolic networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Characterization of complex networks: A survey of measurements
• Hierarchical Organization in Complex Networks
• Self-similarity of complex networks
• Renormalization group analysis of the small-world network model
• Origins of fractality in the growth of complex networks
• Pseudofractal Scale-free Web
• Deterministic Scale-Free Networks
• Small-world networks: Evidence for a crossover picture
• Fractal and Transfractal Recursive Scale-Free Nets
• A Geometric Fractal Growth Model for Scale Free Networks
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Self-similar disk packings as model spatial scale-free networks
• A deterministic small-world network created by edge iterations
• Recursive graphs with small-world scale-free properties
• 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
• High Dimensional Apollonian Networks
• Evolving Apollonian Networks with Small-world Scale-free topologies
• A general geometric growth model for pseudofractal scale-free web
• 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

Cited by in corpus (7)

• Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices
• Exact solution of mean geodesic distance for Vicsek fractals
• Farey Graphs as Models for Complex Networks
• Counting spanning trees in a small-world Farey graph
• Transition from small to large world in growing networks
• Contact graphs of disk packings as a model of spatial planar networks
• Vertex labeling and routing in expanded Apollonian networks