Heterogenous scaling in the inter-event time of on-line bookmarking

In this paper, we study the statistical properties of bookmarking behaviors in Delicious.com  . We find that the inter-event time (ττ) distributions of bookmarking decay in a power-like manner as ττ increases at both individual and population levels. Remarkably, we observe a significant change in the exponent when the inter-event time increases from the intra-day range to the inter-day range. In addition, the dependence of the exponent on individual activity is found to be different in the two ranges. Instead of monotonically increasing with activity  , the inter-day exponent peaks around 3. These results suggest that the mechanisms driving human actions are different in the intra-day and inter-day ranges. We further show that the global distributions of less active users are closer to an exponential distribution than those of more active users. Moreover, a universal behavior in the inter-day range is observed by considering the rescaled variable τ/〈τ〉τ/〈τ〉. Finally, the possible causes of these phenomena are discussed.

► We find that the inter-event time distributions of bookmarking decay in a power-like manner at both individual and population levels.
► A significant change was found in the decay exponent when the inter-event time increases from the intra-day range to the inter-day range.
► The exponent dependence on individual activity follows different trends in the two ranges.
► In the inter-day range, data collapse of the inter-event time distribution is found by rescaling with the average inter-event time.