Fractality and degree correlations in scale-free networks

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2017-07, Vol.90 (7), p.1-9, Article 126
• Main Authors: Fujiki, Yuka, Mizutaka, Shogo, Yakubo, Kousuke
• Format: Article
• Language: English
• Subjects: Complex Systems; Condensed Matter Physics; Correlation; Fluid- and Aerodynamics; Networks; Physics; Physics and Astronomy; Regular Article; Rewiring; Shortest-path problems; Social networks; Solid State Physics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2017-80031-x

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. We show that there are many MD networks with different topologies if the degree sequence is the same with that of the ( u,v )-flower but most of them are not fractal. These results demonstrate 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 the sense of the shortest path distance, in similar degrees.