Evolving small-world scale-free networks consist of cliques

Abstract

We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the networks follow a power-law degree distribution, with degree exponent continuously tuned between 2 and 3. The exact expression of clustering coefficient is also provided for the networks. Furthermore, the investigation of the average path length reveals that the networks possess small-world feature. Interestingly, we find that a special case of our model can be mapped into the Yule process.

References in corpus (38)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Power laws, Pareto distributions and Zipf's law
• The structure of scientific collaboration networks
• Evolution of networks
• Classes of behavior of small-world networks
• Hierarchical Organization in Complex Networks
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Topology of evolving networks: local events and universality
• Connectivity of Growing Random Networks
• Organization of Growing Random Networks
• Pseudofractal Scale-free Web
• Statistical analysis of 22 public transport networks in Poland
• Generic scale of the "scale-free" growing networks
• Bipartite Graphs as Models of Complex Networks
• Maximal planar networks with large clustering coefficient and power-law degree distribution
• Scaling Behaviour of Developing and Decaying Networks
• General Dynamics of Topology and Traffic on Weighted Technological Networks
• Scale-free Networks on Lattices
• Identifying "communities" within energy landscapes
• 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
• Rate equation approach for correlations in growing network models
• Recursive graphs with small-world scale-free properties
• Coherence in scale-free networks of chaotic maps
• Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation
• High dimensional random Apollonian networks
• High Dimensional Apollonian Networks
• The network of concepts in written texts
• 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
• Renormalization group for evolving networks
• Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
• Renormalizing Sznajd model on complex networks taking into account the effects of growth mechanisms
• Synchronous and Asynchronous Recursive Random Scale-Free Nets

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• Exact calculations of first-passage properties on the pseudofractal scale-free web
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• Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks
• Quenched-Vacancy Induced Spin-Glass Order
• Contact graphs of disk packings as a model of spatial planar networks
• Tutte polynomial of pseudofractal scale-free web
• Volatilities analysis of first-passage time and first-return time on a small-world scale-free network
• Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices
• Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds
• Independence number and the number of maximum independent sets in pseudofractal scale-free web and Sierpiński gasket
• Edge Domination Number and the Number of Minimum Edge Dominating Sets in Pseudofractal Scale-Free Web and Sierpiński Gasket