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...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.60872060,11101265)the Shanghai Natural Science Foundation of China(No.12ZR1421000)the Shanghai Education Commission Innovation Project Fund(Nos.12ZZ193,14YZ152,15ZZ099)
文摘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.
