Understanding influence of fractal generative manner on structural properties of tree networks

It is of considerable interest to uncover the influence of generative manners on the topological structure of growth networks in the context of complex networks. In this paper, we consider in detail the fractal generative manner for creating tree networks. First, we present a principled framework in order to create growth tree networks with the fractal feature. Then, some fundamental structural parameters including fractal dimension, diameter, degree distribution and Pearson correlation coefficient on example networks are analyzed in depth. The results suggest that generative manners yielding network with an identical fractal dimension have a remarkable influence on other structural parameters. Next, we study two kinds of stochastic fractal tree networks Ttin and Ttout. The former is built based on in-group mixing generative manners, and the latter is based on out-group mixing. Particularly, we derive the closed-form solution to mean hitting time for random walks on network Ttin and determine degree distribution on network Ttout. The results show that fractal feature plays a key role in the first model compared to the preferential attachment mechanism, however, the opposite consequence can be obtained in the other model. Finally, we conduct extensive experiments, which suggests that computer simulations are in good agreement with theoretical analysis.