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

Another of my papers just came out in final form today. Here are some details.

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

Authors: Xinzhe Zuo and Mason A. Porter

Abstract: The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, 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 moments of the tie strength evolve 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 the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible–infected–recovered model of an infectious disease.