  Intervals between discrete events representing human activities, as well as
other types of events, often obey heavy-tailed distributions, and their impacts
on collective dynamics on networks such as contagion processes have been
intensively studied. The literature supports that such heavy-tailed
distributions are present for inter-event times associated with both individual
nodes and individual edges in networks. However, the simultaneous presence of
heavy-tailed distributions of inter-event times for nodes and edges is a
non-trivial phenomenon, and its origin has been elusive. In the present study,
we propose a generative model and its variants to explain this phenomenon. We
assume that each node independently transits between a high-activity and
low-activity state according to a continuous-time two-state Markov process and
that, for the main model, events on an edge occur at a high rate if and only if
both end nodes of the edge are in the high-activity state. In other words, two
nodes interact frequently only when both nodes prefer to interact with others.
The model produces distributions of inter-event times for both individual nodes
and edges that resemble heavy-tailed distributions across some scales. It also
produces positive correlation in consecutive inter-event times, which is
another stylized observation for empirical data of human activity. We expect
that our modeling framework provides a useful benchmark for investigating
dynamics on temporal networks driven by non-Poissonian event sequences.
