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

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