电气工程及其自动化专业毕业设计（论文）外文翻译_精品.doc

英 文 翻 译 2010 届 电气工程及其自动化 专业 1006972 班级 姓 名 学号 指导教师 职称 二О一 二 年 二 月 十 日 2.3. Networks models The observations described in the examples of Section 2.2 have clearly motivated the introduc tion of new concepts and models. In this section, we focus on the mathematical modelling of netw -orks, discussing some simple and genericmodels from the point of view of their motivation, const- ruction procedure and signi?cant properties. Further details on models can be found in Refs. [2–4,7]. 2.3.1. Random graphs The systematic study of random graphs was initiated by Erd?s and Rényi in 1959 with the orig- inal purpose of studying, by means of probabilistic methods, the properties of graphs as a function of the increasing number of random connections. The term random graph refers to the disordered nature of the arrangement of links between different nodes. In their ?rst article, Erd?s and Rényi proposed a model to generate random graphs with N nodes and K links, that we will henceforth call Erd?s and Rényi (ER) random graphs and denote as GERN,K . Starting with N disconnected nodes, ER random graphs are generated by connecting couples of randomly selected nodes, prohibiting multiple conne- ctions, until the number of edges equals K [115]. We emphasize that a given graph is only one out come of the many possible realizations, an element of the statistical ensemble of all possible combin- ations of connections. For the complete description of K,None would need to describe the ensembleof possible realizations, that is, in the matricial representation, the ensemble of adjacency matrices [116]. An alternative model for ER random graphsconsists in connecting each couple of nodes with a probability 0 p 1. This procedure de?nes a different ensemble, denoted as G N,pand containing graphs with different of links:graphs with K links will appear in the ensemble with a probability pK(1 ? p)N (N ?1)/2?K [14,115,117]. The two models have a