  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.
