具有去边机制的随机—无标度混合演化网络度分布
代写硕士论文-【摘要】 复杂网络可以描述自然界和社会中的各种网络,如因特网、新陈代谢网络,社会关系网络等,因此,复杂网络已经成为学术研究的一个热点,其理论广泛应用于各个领域。近年来,真实网络中的无标度特性的发现更是激起了学术界对复杂网络的研究热潮。本篇硕士学位论文将研究具有去边机制的随机一无标度的混合网络演化模型：该模型的网络初始含有m0个节点,其总度数N0=m0(m0-1),每一个时间步增加一个含有m条边的新节点,新节点以概率p与旧节点进行随机连接,以概率1-p与旧节点进行择优连接,择优规则同BA模型,每一个时间步,删除一条旧连接lij,节点i择优选择,其择优概率Π’(ki)同BA模型,节点j在i的邻域内随机选择。笔者认为,前人利用主方程法求解该模型的度分布仍有值得商榷之处。笔者利用马氏链方法和技巧严格证明在此情形下,模型稳态度分布的存在性、无标度性以及标度指数,并给出它的精确解,并指出网络的无标度性是否取决于参数p和m。
硕士论文代写-【Abstract】 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.