Anomalous random networks

TL;DR

This paper introduces a novel time-varying anomalous random network model that captures node inactivity durations and analyzes phenomena like gift delivery and viral spread, offering new insights into network dynamics.

Contribution

It proposes a dinner party anomalous random networks model with analytical solutions for node activity durations, advancing the understanding of complex network behaviors.

Findings

Derived the probability density function for node activity times.

Analyzed gift delivery and viral transmission in the new network model.

Provided quantitative insights into random network dynamics.

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.