Research On The Evolving Model Of Scale-free Networks

As an important tool for studying complexity problem, in recent years, Complex network hasattracted a lot of attention. In our real world, there are many Complex system exists, such as aviationnetwork, network, social network and so on. And most people have the study of complex networkson evolving mechanism and the topological properties. Empirical study shows that, in reality, manycomplex networks are scale-free networks which have a thick tail in its degree distribution curve.Therefore, to study the evolving model of scale-free network has great practical value and practicalsignificance.BA model displays a lot of limitations in the application, only with evolving mechanism ofgrowth and preferential attachment. In this paper, we put forward to two models in order toStrengthen the practicality. One is increasing network which has old edges rewired and new edgesadded in the original nodes. The other is the two-way evolution model of a BA scale-free network isgiven, which considers both new edges increasing and old edges removing.In this paper, we analyze the degree distribution of improved models with the mean field theory.The results show that degree distribution of both improved models obeys the power law distribution.Among them, the growth model generates more nodes of big degree, compared with the BAmodel.The reason is that old edges rewired and new edges added in the original nodes can make bignode degrees bigger, that is to say, the rich get richer. Theoretical deduction and numericalsimulation shows that the two-way evolution model of a BA scale-free network obeys powerdistribution and the power exponent is between1and3, which broaden the range of application.And we can get that the model emerges the characteristics of the real network including small worldcharacteristics and small average path length, by contrast of the basic BA model. At the last, weanalyze the robustness and vulnerability to the integrated two improved model and the resultshows that the integrated scale-free network has strong robustness to random failures but fragile todeliberate attack.