A Scale-free Network Model with Hierarchical Structure

The discovery of the scale-free network made people into a new area on the complex network.For further describing the structure of the real network topology,this paper mainly studied evolution mechanism of the complex network,proposed a method to generate hierarchical network by edge iterations.Also,it deduced some particular statistical characteristics of the hierarchy based on the algorithm,generated the simulated network with computer and contrasted the different size of the statistical characteristics of the simulated network.In addition,both theoretical analysis and numerical simulation show that the hierarchical model follows a power-law degree distribution with the degree exponent continuously tuned between 2 and 3,and the shortest length path increases logarithmically with the number of nodes and the high clusting coefficient.The simulation results are given,which are in agreement with the theoretic calculations.As a result,the model with hierarchical structure can efficiently describe the real network,and the scaling-free and high clustering features in the real network are the self-organiztion result of the hierarchical network.