With A Random Mechanism To The Side - Scale-free Mixing Evolution Of The Network Degree Distribution

Networks exist in every aspect of nature and society. Most of the systems, e.g.WWW, social relationship networks,biological neural networks and so on, can be described as complex network. Thus, complex network attracts much attention from all research circles and have found many potential applications in a variety of fields.Recently, the discovery of scale-free character in real-life network stimulate more researchers' interest.In this paper,the auther proposes a evolving network with link additions as well as removals and both random and preferential attachment.The model start with a small number(m0)of vertices,which has a total degree No=m0(m0-1).,a new edges with m new edges is added to the system at each time step with edges connected to an old vertex i determined by the attachment probability Where p is a parameter characterizing the relative weights between the deterministic and random contributions toΠ(kt(t)),and we select a vertex i with probabilityΠ(ki) is similar to BA model,and a vertex j randomly in the domain of i,then remove the edge lij. Based on the concept and techniques of Markov chain theory,the auther give the rigorous proof for the degree distribution and scaling exponent of the network and show the relationship between scaling exponent and the parameters p and m of the evolving network with link additions as well as removals and both random and preferential attachment The network will self-organize into a scale-free state if involve the aspect of the preferential attachment (i.e.l-p>0),and the scaling exponent is not a constant but varies with the parameters p and m.