Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection

Abstract

The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the mean tie strength evolves with time in several models, and we explore -- both numerically and analytically -- criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of interaction patterns of our continuous-time networks on contagion dynamics in a susceptible-infected-recovered model of an infectious disease.

arXiv commentrevised version

References in corpus (9)

• Epidemic processes in complex networks
• Temporal Networks
• Modern temporal network theory: A colloquium
• Recent advances in percolation theory and its applications
• Social Contagion: An Empirical Study of Information Spread on Digg and Twitter Follower Graphs
• Limited path percolation in complex networks
• A Hebbian approach to complex network generation
• Tempus Volat, Hora Fugit -- A Survey of Tie-Oriented Dynamic Network Models in Discrete and Continuous Time
• Opinion dynamics on tie-decay networks

Cited by in corpus (3)

• From temporal network data to the dynamics of social relationships
• Opinion dynamics on tie-decay networks
• Spline tie-decay temporal networks