  Models of complex networks often incorporate node-intrinsic properties
abstracted as hidden variables. The probability of connections in the network
is then a function of these variables. Real-world networks evolve over time,
and many exhibit dynamics of node characteristics as well as of linking
structure. Here we introduce and study natural temporal extensions of static
hidden-variable network models with stochastic dynamics of hidden variables and
links. The rates of the hidden variable dynamics and link dynamics are
controlled by two parameters, and snapshots of networks in the dynamic models
may or may not be equivalent to a static model, depending on the location in
the parameter phase diagram. We quantify deviations from static-like behavior,
and examine the level of structural persistence in the considered models. We
explore temporal versions of popular static models with community structure,
latent geometry, and degree-heterogeneity. We do not attempt to directly model
real networks, but comment on interesting qualitative resemblances, discussing
possible extensions, generalizations, and applications.
