Fig. 1.

Measuring the speed of hashtag dynamics: a Daily usage L_i(t) of the top 50 hashtags i on Twitter in 2016, with exemplary highlighted major events. b Average trajectories 〈L(t − t_peak)〉 leading to a local maximum L_i(t_peak) in all top hashtags from 2013 to 2016. The shaded area shows the 95% confidence intervals (CI). In the background a 1% random sample of trajectories is shown in grey. c Temporal density of extreme events (local maxima with a lower threshold for the slopes, for details see Methods section), scattered over 365 days. d Distribution of daily relative losses $P\left(\Delta L_i^{\left(\mathrm{l}\right)}∕L_i\right)$ and e daily relative gains $P\left(\Delta L_i^{\left(\mathrm{g}\right)}∕L_i\right)$. The solid lines show fitted log-normal distributions $P\left(x\right)=1∕\left(x\sigma \sqrt{2\pi }\right)\exp \left[-{\left(\mathrm{ln(x)}-\mu \right)}^2∕\left(2{\sigma }^2\right)\right]$ (distributions truncated at 10⁻³). Inset: The corresponding distributions of the local maxima of each hashtag trajectory P(L_i(t_peak)) (distributions truncated at 10³). Source data are provided as a Source Data file and in an online repository (see data availability statement)