Topological multifractal in realistic networks with explain by diffusion limited aggregation mechanism

Recent studies indicate that many realistic networks exhibit novel topological structure features by self-similar. In this paper, we investigate the diffusion limited aggregation(DLA) mechanism which is used to generate topological fractal networks. Interestingly, we find that the presented model performs multi-fractal property by the application of a renormalization procedure that coarse grains the system into boxes containing nodes within a given size. Further analysis shows that many real world networks, such as WWW, scientists collaboration network, metabolic network, protein-protein interaction network and Internet in the routing level or autonomy system level, can also be characterized by multi-fractal.