  Complex networks have recently attracted much attention in diverse areas of
science and technology. Many networks such as the WWW and biological networks
are known to display spatial heterogeneity which can be characterized by their
fractal dimensions. Multifractal analysis is a useful way to systematically
describe the spatial heterogeneity of both theoretical and experimental fractal
patterns. In this paper, we introduce a new box covering algorithm for
multifractal analysis of complex networks. This algorithm is used to calculate
the generalized fractal dimensions $D_{q}$ of some theoretical networks, namely
scale-free networks, small world networks and random networks, and one kind of
real networks, namely protein-protein interaction networks of different
species. Our numerical results indicate the existence of multifractality in
scale-free networks and protein-protein interaction networks, while the
multifractal behavior is not clear-cut for small world networks and random
networks. The possible variation of $D_{q}$ due to changes in the parameters of
the theoretical network models is also discussed.
