Continuous-Time Independent Edge-Markovian Random Graph Process

• Published in: Chinese annals of mathematics. Serie B Vol. 37; no. 1; pp. 73 - 82
• Main Authors: Du, Ruijie, Wang, Hanxing, Fu, Yunbin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2016; School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620, China%School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai 201620,China; Department of Mathematics, Shanghai University, Shanghai 200444, China
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; 分布序列; 平稳分布; 独立边; 节点连接; 过程模型; 连续时间; 随机图; 马尔可夫; Random graph process; Independent edge-Markovian random graph process; 05C80; Complex networks; Random graph; Stationary distribution
• ISSN: 0252-9599; 1860-6261
• DOI: 10.1007/s11401-015-0941-5

In this paper, the continuous-time independent edge-Markovian random graph process model is constructed. The authors also define the interval isolated nodes of the random graph process, study the distribution sequence of the number of isolated nodes and the probability of having no isolated nodes when the initial distribution of the random graph process is stationary distribution, derive the lower limit of the probability in which two arbitrary nodes are connected and the random graph is also connected, and prove that the random graph is almost everywhere connected when the number of nodes is sufficiently large.