Statistical Research On Fractal Characteristic Of Complex Networks

At present, the research on complex networks has been expanded to a variety ofdifferent fields. Research methods have developed variously. With these methodsand powerful computing ability of the computer, the research on complex networkhas become deeper and deeper. From the research on structure characteristic of thesmall-world and scale-free network, the basic topological structure of complexnetworks has been the focus of research. With the in-depth study of complexnetworks, the self-similar fractal characteristic of complex networks has beenexcavated. The research on complex networks has come to a new stage.This paper focuses on the research of the fractal characteristic of complexnetworks. We analyze the origin and the authentication of fractal characteristic ofcomplex networks, apply some weight-adding methods to different network modelsand compare the results between original networks and weighted networks. Finally,we put forward a complex network topology reconstruction algorithm to adjust thenetwork structures and make them fractal.Firstly, we introduce the basic statistical characteristics of complex networksand several common complex network models. Then, we describe the fractalcharacteristic and the application of the renormalization group method to complexnetworks. We construct a new kind of network model with scale-free and fractalcharacteristics.Secondly, exploring the origin of fractality in complex networks. Here weintroduce three box-covering algorithms: compact-box-burning algorithm, greedycoloring algorithm, and MEMB algorithm. We improve the MEMB algorithm andapply it to the complex networks which are weighted with the AdjustCD and WDmethods. The results of protein-protein interaction networks and fractal networkgrowth models prove that it is also effective in verifying the existence of fractalityin complex networks.Lastly, we select the skeleton of a complex network as the target and study therelations of complex network and its skeleton tree. It is proved that a fractalcomplex network contains a fractal skeleton tree. Also, a complex network can beregarded as a skeleton tree with lots of different types of shortcuts–local shortcutsand global shortcuts. Fractal and non-fractal complex networks show two differenttypes of shortcuts length distribution. Furthermore, we design an algorithm toreconstructe the topological structure of a complex network based on its skeleton tree. This algorithm can adjust the topological structure of a complex network andtransform it from non-fractal to fractal.In this paper, we extend the box-covering algorithms to the real number field tomake it suitable for a weighted network. Moreover, we design a complex networktopology reconstruction algorithm based on the skeleton structure. It can effectivelyadjust a complex network structure and make it fractal.