文章基本信息

标题：A random graph of moderate density
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作者：Ágnes Backhausz ; Tamás F. Móri
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2022
卷号：27
页码：1-12
DOI：10.1214/21-ECP444
语种：English
出版社：Electronic Communications in Probability
摘要：We analyse a randomly growing graph model in which the average degree is asymptotically equal to a constant times the square root of the number of vertices, and the clustering coefficient is rather small. In every step, we choose two vertices uniformly at random, check whether they are connected or not, and we either add a new edge or delete one and add a new vertex of degree two to the graph. This dependence on the status of the connection chosen vertices makes the total number of vertices random after n steps. We prove asymptotic normality for this quantity and also for the degree of a fixed vertex (with normalization n1∕6). We also analyse the proportion of vertices with degree greater than a fixed multiple of the average degree, and the maximal degree.
关键词：05C80;degree distribution;intermediate density;Random graphs