Temporal networks with node-specific memory: Unbiased inference of transition probabilities, relaxation times, and structural breaks

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, suboptimal 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 real-world social networks, 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.