title: Multifractality of complex networks.
abstract: We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass exponents τ(q) for several deterministic, stochastic, and real-world fractal scale-free networks are nonlinear functions of q, which implies that structural measures of these networks obey the multifractal scaling. In addition, we give a general expression of τ(q) for some class of fractal scale-free networks by a mean-field approximation. The multifractal property of network structures is a consequence of large fluctuations of local node density in scale-free networks.
authors: Department of Mathematical Informatics, The University of Tokyo, Tokyo 113-8656, Japan. sfuruya@stat.t.u-tokyo.ac.jp
authors: Shuhei
authors: S
authors: Furuya
authors: Kousuke
authors: K
authors: Yakubo