Generative models of simultaneously heavy-tailed distributions of inter-event times on nodes and edges

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.