Fractality and degree correlations in scale-free networks

Abstract

Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine the possibility that disassortativity in complex networks is the origin of fractality. To this end, maximally disassortative (MD) networks are prepared by rewiring edges while keeping the degree sequence of an initial uncorrelated scale-free network that is guaranteed to become fractal by rewiring edges. Our results show that most of MD networks with different topologies are not fractal, which demonstrates that disassortativity does not cause the fractal property of networks. In addition, we suggest that fractality of scale-free networks requires a long-range repulsive correlation in similar degrees.

9 pages, 7 figures

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Cited by in corpus (10)

• Disassortativity of percolating clusters in random networks
• Scaling theory of fractal complex networks
• A general formulation of long-range degree correlations in complex networks
• Structure of percolating clusters in random clustered networks
• Emergence of Long-Range Correlations in Random Networks
• Analytic solution of the two-star model with correlated degrees
• Identification of intrinsic long-range degree correlations in complex networks
• Percolation on a maximally disassortative network
• Bifractality of fractal scale-free networks
• Simple model of fractal networks formed by self-organized critical dynamics