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 (τ) distributions of bookmarking decay in a power-like manner as τ 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〉. Finally, the possible causes of these phenomena are discussed.