  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.
