Recursive graphs with small-world scale-free properties

Abstract

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.

4 pages, 2 figures

References in corpus (13)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The diameter of the world wide web
• The large-scale organization of metabolic networks
• Hierarchical Organization in Complex Networks
• Pseudofractal Scale-free Web
• Deterministic Scale-Free Networks
• Classification of scale-free networks
• Generic scale of the "scale-free" growing networks
• A Geometric Fractal Growth Model for Scale Free Networks
• Deterministic Small-World Networks
• Exact scaling properties of a hierarchical network model
• Characterizing the structure of small-world networks

Cited by in corpus (43)

• Self-similar disk packings as model spatial scale-free networks
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• A deterministic small-world network created by edge iterations
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Characterizing the network topology of the energy landscapes of atomic clusters
• Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation
• High dimensional random Apollonian networks
• On the spectrum of the normalized Laplacian of iterated triangulations of graphs
• 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
• Exact analytical solution of average path length for Apollonian networks
• Farey Graphs as Models for Complex Networks
• Evolving small-world scale-free networks consist of cliques
• Weighted Network of Chinese Nature Science Basic Research
• Evolving small-world networks with geographical attachment preference
• Growing Scale-free Small-world Networks with Tunable Assortative Coefficient
• Degree-dependent intervertex separation in complex networks
• A directed network model for World-Wide Web
• Local-world evolving networks with tunable clustering
• Correlations in random Apollonian network
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Deterministic hierarchical networks
• Complex Network Properties of Chinese Natural Science Basic Research
• Multistage Random Growing Small-World Networks with Power-law degree Distribution
• Recursive weighted treelike networks
• A geometric growth model interpolating between regular and small-world networks
• Deterministic weighted scale-free small-world networks
• Minimal models of weighted scale-free networks
• Planar unclustered scale-free graphs as models for technological and biological networks
• Synchronous and Asynchronous Recursive Random Scale-Free Nets
• Stochastic and mixed flower graphs
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Tuning degree distributions of scale-free networks
• A star based model for the eigenvalue power law of Internet graphs
• Vertex labeling and routing in expanded Apollonian networks
• Constructions and properties of a class of random scale-free networks
• Characteristics of Preferentially Attached Network Grown from Small World
• Deterministic scale-free networks created in a recursive manner
• Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web
• Self-similar planar graphs as models for complex networks
• Two Cumulative Distributions For Scale-freeness of Dynamic Networks