Anomalous random networks

Abstract: After the groundbreaking work of Erd$\ddot{o}$s-R$\acute{e}$nyi random graph, the random networks has made great progress in recent years. One of the eye-catching modeling is time-varying random network model capable of encoding the instantaneous time description of the network dynamics. To further describe the random duration time for the nodes to be inactive, we herein propose a dinner party anomalous random networks model, and derive the analytical solution of the probability density function for the node being active at a given time. Moreover, we investigate the gift delivery and viral transmission in dinner party random networks. This work provides new quantitative insights in describing random networks, and could help model other uncertainty phenomena in real networks.