The Reseach On The Existence Of Multi-fractal Characteristics Of Complex Networks

At present, the research on complex networks has been expanded to different fields. With the development of computer technology and the variety of research methods and instruments, the research on complex networks has been deepened in all related fields, which make us better to know how the world work and how complex the environment around us is. Certainly, with knowing and using the mechanism about the complex networks around us, we can change the world and make our lives better. Although variety of research methods and direction. The research on topological structure of complex network has been a very important research contents. However, there is less researches on multi-fractal characteristic of complex networks.This paper focuses on the research of multi-fractal characteristic of complex networks. In this paper, complex network is translated into time series, and the detrending moving average algorithm is used to research the multi-fractal characteristic of generated time series. Through the research above, the multi-fractal characteristic of complex networks is easy to attain.This paper, firstly, introduces some basic theoretical knowledge about complex networks, then uses the research method introduced above to prove that multi-fractal phenomenon does exist in complex networks. For the most common scale-free network in reality world, the paper researches the existence of multi-fractal characteristic of scale-free network and how some statistics of complex networks influence the existence of multi-fractal characteristic. At last, the paper finds that the assortatively coefficient has relationship with the existence of the multi-fractal characteristic of scale-free network.After the above research work, the paper begins to research the existence of multi-fractal characteristic in two types of small-world networks, namely WS model and NW model, and find neither of the type networks has multi-fractal phenomenon. The paper also researches the influence of assortatively coefficient’s change to multi-fractal characteristic. For WS small-world network that is neither fractal nor multi-fractal, this paper will get shortcut between two disconnected nodes by adding edge with one probability distribution, and research the fractal and multi-fractal characteristics of the WS network after adding edges.This paper innovatively uses the finite-memory random walk to translate complex networks into time series, and researches the multi-fractal characteristic of the original network through researching multi-fractal characteristic of generated time series. The method is effective to examine and prove the multi-fractal characteristic of complex networks.