Transition from fractal to non-fractal scalings in growing scale-free networks

Abstract

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.

arXiv comment7 pages, 3 figures, definitive version accepted for publication in EPJB

References in corpus (21)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Characterization of complex networks: A survey of measurements
• Self-similarity of complex networks
• Universal Behavior of Load Distribution in Scale-free Networks
• Origins of fractality in the growth of complex networks
• Growing Scale-Free Networks with Small World Behavior
• Average path length in random networks
• Average path length in uncorrelated random networks with hidden variables
• 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
• Percolation in Hierarchical Scale-Free Nets
• Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
• Optimal Path and Minimal Spanning Trees in Random Weighted Networks
• Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices
• Griffiths singularities and algebraic order in the exact solution of an Ising model on a fractal modular network
• Preferential attachment during the evolution of a potential energy landscape

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• Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks
• Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks
• Exact eigenvalue spectrum of a class of fractal scale-free networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• An alternative approach to determining average distance in a class of scale-free modular networks
• Investigating the Origins of Fractality Based on Two Novel Fractal Network Models