Temporal network modeling with online and hidden vertices based on the birth and death process

TL;DR

This paper models temporal networks with online and hidden vertices using birth-death processes, revealing stable distributions and regular patterns in degree distributions, with applications to real-world networks.

Contribution

It introduces a novel model for temporal networks with online and hidden states based on birth-death processes, providing analytical insights and simulation validation.

Findings

Online neighbor counts are stable and follow homogeneous distributions.

Degree distributions exhibit regular patterns in small-world and scale-free networks.

Model effectively fits real-world network data.

Abstract

Complex networks have played an important role in describing real complex systems since the end of the last century. Recently, research on real-world data sets reports intermittent interaction among social individuals. In this paper, we pay attention to this typical phenomenon of intermittent interaction by considering the state transition of network vertices between online and hidden based on the birth and death process. By continuous-time Markov theory, we show that both the number of each vertex's online neighbors and the online network size are stable and follow the homogeneous probability distribution in a similar form, inducing similar statistics as well. In addition, all propositions are verified via simulations. Moreover, we also present the degree distributions based on small-world and scale-free networks and find some regular patterns by simulations. The application in fitting real networks is discussed.