Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history

The origin of non-Poissonian or bursty temporal patterns observed in various data sets for human social dynamics has been extensively studied, yet its understanding still remains incomplete. Considering the fact that humans are social beings, a fundamental question arises: Is the bursty human dynamics dominated by individual characteristics or by interaction between individuals? In this paper we address this question by analyzing the Wikipedia edit history to see how spontaneous individual editors are in initiating bursty periods of editing, i.e., individual-driven burstiness, and to what extent such editors' behaviors are driven by interaction with other editors in those periods, i.e., interaction-driven burstiness. We quantify the degree of initiative (DoI) of an editor of interest in each Wikipedia article by using the statistics of bursty periods containing the editor's edits. The integrated value of the DoI over all relevant timescales reveals which is dominant between individual-driven and interaction-driven burstiness. We empirically find that this value tends to be larger for weaker temporal correlations in the editor's editing behavior and/or stronger editorial correlations. These empirical findings are successfully confirmed by deriving an analytic form of the DoI from a model capturing the essential features of the edit sequence. Thus our approach provides a deeper insight into the origin and underlying mechanisms of bursts in human social dynamics.

Figure 1

Diagram for the data analysis procedure. (a) Part of the preprocessed data of Wikipedia edit history. Each line contains the time stamp, article ID, and editor ID of the edit. (b) Part of the edit sequence of a given article (e.g., article 5 042 951) containing the time stamp and the editor ID per edit. (c) Visualization of part of the edit sequence for article 5 042 951. Each edit is denoted by a vertical line in the horizontal time axis. Among editors who edited the article, we choose a particular editor or ego (e.g., editor 13 014), while all other editors are called alters. Edits by the ego and alters are denoted by red solid lines and blue dotted lines, respectively. For a given timescale $\mathrm{\Delta }t$, bursts are detected and categorized into three groups: initiated (red area), uninitiated-but-involved (orange area), and uninvolved bursts (blue area). (d) The degree of initiative (DoI), $r$ in Eq. (1), for editor 13 014 in article 5 042 951, with $\mathrm{\Delta }t$ in seconds. See the text for the definitions of $\mathrm{\Delta }{t}_1$ and $\mathrm{\Delta }{t}_2$. (e) The DoI curve as a function of the normalized timescale $\mathrm{\Delta }{t}^{\prime }$ in Eq. (2), from which the area under the DoI curve is calculated as $\approx$0.45.

Figure 2

(a) Heat map of the number of article-ego pairs having the same characteristic timescales $\mathrm{\Delta }{t}_1$ and $\mathrm{\Delta }{t}_2$. (b) Heat map of the averaged value of the area under the DoI curve, denoted by $\langle \mathrm{AUC}\rangle$, for the pairs having the same characteristic timescales $\mathrm{\Delta }{t}_1$ and $\mathrm{\Delta }{t}_2$. In panels (a) and (b), log-binned $\mathrm{\Delta }{t}_1$ and $\mathrm{\Delta }{t}_2$ have been used for the calculation. Both horizontal and vertical dashed lines denote one day. (c)–(e) Heat maps of the number of article-ego pairs in the spaces of ($B_{{}_{\mathrm{E}}}$, AUC) (c), ($B_{{}_{\mathrm{A}}}$, AUC) (d), and ($M_c$, AUC) (e). See the text for the definitions of $B_{{}_{\mathrm{E}}}$, $B_{{}_{\mathrm{A}}}$, and $M_c$. In each of panels (c)–(e), we also present the value of the Pearson correlation coefficient (PCC). (f) Heat map of $\langle \mathrm{AUC}\rangle$ for the pairs having the same values of $B_{{}_{\mathrm{E}}}$ and $M_c$. In all panels the gray color means no data in the area.

Figure 3

(a) Part of time series for the article-ego pair that is characterized by small $B_{{}_{\mathrm{E}}}$ and large $M_c$ (hence, individual-driven burstiness). (b) Part of time series for the article-ego pair that is characterized by large $B_{{}_{\mathrm{E}}}$ and small $M_c$ (hence, interaction-driven burstiness). Red (blue) vertical lines denote the ego's (the alter's) edits. Time intervals have been chosen to contain 20–30 edits by the ego in both cases.

Figure 4

(a)–(c) Analytic results of the DoI curve of the model in Eq. (30) using $P_{{}_{\mathrm{E}}}\left(\tau \right)$ and $P_{{}_{\mathrm{A}}}\left(\tau \right)$ both in a form of the power-law distribution with exponential cutoff in Eq. (31) (solid curves). In all cases we use $q_{{}_{\mathrm{E}}}=0.1$, ${\tau }_{\min }=2^2$, and ${\tau }_{\mathrm{c}}=2^{10}$ for $P_{{}_{\mathrm{E}}}\left(\tau \right)$, and ${\tau }_{\min }=1$ and ${\tau }_{\mathrm{c}}=2^{15}$ for $P_{{}_{\mathrm{A}}}\left(\tau \right)$. We plot the DoI curves for several values of ${\alpha }_{{}_{\mathrm{E}}}$ when $q_{{}_{\mathrm{E}|\mathrm{E}}}=0.1$ and ${\alpha }_{{}_{\mathrm{A}}}=1.5$ (a), for several values of ${\alpha }_{{}_{\mathrm{A}}}$ when $q_{{}_{\mathrm{E}|\mathrm{E}}}=0.1$ and ${\alpha }_{{}_{\mathrm{E}}}=1.5$ (b), and for several values of $q_{{}_{\mathrm{E}|\mathrm{E}}}$ when ${\alpha }_{{}_{\mathrm{E}}}={\alpha }_{{}_{\mathrm{A}}}=1.5$ (c). These analytic results are confirmed by the simulation results from 100 generated edit sequences of up to $n=2^{23}$ edits (symbols). The error bars denote the standard deviations. (d)–(f) Numerical results of the AUC value calculated from the analytic result of the DoI curve in Eq. (30) for various combinations of the parameter values, i.e., in the space of $({\alpha }_{{}_{\mathrm{A}}},{\alpha }_{{}_{\mathrm{E}}})$ when $q_{{}_{\mathrm{E}}}=q_{{}_{\mathrm{E}|\mathrm{E}}}=0.1$ (d), in the space of $(q_{{}_{\mathrm{E}}},q_{{}_{\mathrm{E}|\mathrm{E}}})$ when ${\alpha }_{{}_{\mathrm{E}}}={\alpha }_{{}_{\mathrm{A}}}=1.5$ (e), and in the space of $({\alpha }_{{}_{\mathrm{E}}},q_{{}_{\mathrm{E}|\mathrm{E}}})$ when $q_{{}_{\mathrm{E}}}=0.1$ and ${\alpha }_{{}_{\mathrm{A}}}=1.5$ (f). In all cases we use ${\tau }_{\min }=2^2$ and ${\tau }_{\mathrm{c}}=2^{10}$ for $P_{{}_{\mathrm{E}}}\left(\tau \right)$ and ${\tau }_{\min }=1$ and ${\tau }_{\mathrm{c}}=2^{15}$ for $P_{{}_{\mathrm{A}}}\left(\tau \right)$. The gray area in panel (e) shows the nonexistent parameter space due to conditions in Eqs. (5, 6, 7).

Figure 5

(a) Nonmonotonic dependence of the burstiness parameter $B$ in Eq. (32) on the power-law exponent $\alpha$ for the IET distribution given by Eq. (31) with ${\tau }_{\min }=1$ and various values of ${\tau }_c$. (b) The aggregate distribution of IETs followed by the ego's edits over all article-ego pairs (red circles), with the estimated values of power-law exponent ${\alpha }_{{}_{\mathrm{E}}}=1.15\left(1\right)$ (depicted by a dashed line) and burstiness measure $B_{{}_{\mathrm{E}}}\approx 0.69$. (c) The aggregate distribution of IETs followed by the alters' edits over all article-ego pairs (red circles), with the estimated values of power-law exponent ${\alpha }_{{}_{\mathrm{A}}}=1.11\left(2\right)$ (depicted by a dashed line) and burstiness measure $B_{{}_{\mathrm{A}}}\approx 0.74$.