  One of the main challenges in the study of time-varying networks is the
interplay of memory effects with structural heterogeneity. In particular,
different nodes and dyads can have very different statistical properties in
terms of both link formation and link persistence, leading to a superposition
of typical timescales, sub-optimal parametrizations and substantial estimation
biases. Here we develop an unbiased maximum-entropy framework to study
empirical network trajectories by controlling for the observed structural
heterogeneity and local link persistence simultaneously. An exact mapping to a
heterogeneous version of the one-dimensional Ising model leads to an analytic
solution that rigorously disentangles the hidden variables that jointly
determine both static and temporal properties. Additionally, model selection
via likelihood maximization identifies the most parsimonious structural level
(either global, node-specific or dyadic) accounting for memory effects. As we
illustrate on a real-world social network, this method enables an improved
estimation of dyadic transition probabilities, relaxation times and structural
breaks between dynamical regimes. In the resulting picture, the graph follows a
generalized configuration model with given degrees and given time-persisting
degrees, undergoing transitions between empirically identifiable stationary
regimes.
