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Fig. 13 | Computational Social Networks

Fig. 13

From: Tracking online topics over time: understanding dynamic hashtag communities

Fig. 13

Average times of stable ranks and exemplary trajectories: a the analytic lower bound from Eq. (12), the resulting times from the Monte-Carlo simulation and the empirical values of the normalized average time \(\langle \tau (r) \rangle\) of stable ranking r. The values are normalized to their maximum at \(r=1\) to make them comparable. The inset shows the same plot with logarithmic axes. b Two trajectories from the simulation that reach different maximal ranks. The size \(S_i(t)\) in black and the rank \(r(S_i(t)-(t-t_i))\) in green, which reaches a maximum of \(r=2.\) The inset shows the same quantities for an item that reaches only \(r=6\)

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