  Human social interactions tend to vary in intensity over time, whether they
are in person or online. Variable rates of interaction in structured
populations can be described by networks with the time-varying activity of
links and nodes. One of the key statistics to summarize temporal patterns is
the inter-event time (IET), namely the duration between successive pairwise
interactions. Empirical studies have found IET distributions that are
heavy-tailed (or "bursty"), for temporally varying interaction, both physical
and digital. But it is difficult to construct theoretical models of
time-varying activity on a network that reproduces the burstiness seen in
empirical data. Here we develop a spanning-tree method to construct temporal
networks and activity patterns with bursty behavior. Our method ensures a
desired target IET distribution of single nodes/links, provided the
distribution fulfills a consistency condition, regardless of whether the
underlying topology is static or time-varying. We show that this model can
reproduce burstiness found in empirical datasets, and so it may serve as a
basis for studying dynamic processes in real-world bursty interactions.
