Dynamical strength of social ties in information spreading

We investigate the temporal patterns of human communication and its influence on the spreading of information in social networks. The analysis of mobile phone calls of 20 million people in one country shows that human communication is bursty and happens in group conversations. These features have the opposite effects on the reach of the information: while bursts hinder propagation at large scales, conversations favor local rapid cascades. To explain these phenomena we define the dynamical strength of social ties, a quantity that encompasses both the topological and the temporal patterns of human communication.

Figure 1

Schematic view of communication events around an individual $i$: Each vertical segment indicates an event between $i\to j$ (top) and $*\to i$ (bottom). At each $t_{\alpha }$ in the $*\to i$ time series, ${\tau }_{\mathit{ij}}$ is the time elapsed to the next $i\to j$ event, which is different from the interevent time $\delta t_{\mathit{ij}}$ in the $i\to j$ time series. The shaded area represents the recovery time window $T_i$ after $t_{\alpha }$.

Figure 2

Distribution of the relay time intervals ${\tau }_{\mathit{ij}}$ (main part) and of the interevent times $\delta t_{\mathit{ij}}$ (inset) in the $i\to j$ tie rescaled by ${\stackrel{̲}{\delta t}}_{\mathit{ij}}$. The open circles correspond to the real data, while the open squares are the overall shuffled results. Open diamonds correspond to the case in which only the $*\to i$ sequence is randomized. Only ties with $w_{\mathit{ij}}⩾10$ are considered. In both graphs the dashed line corresponds to the $e^{-x}$ function.

Figure 3

Average size dynamics for (a) a large and (b) a small value of $\lambda$ (left) and the maximum size (right) of the infection outbreaks (over ${10}^4$ realizations) for the real-time data (lines with open circles) and shuffled-time data (lines with open squares) for $T=2$ days. The dashed line shows the critical point estimation of the percolation transition given by $R_1[\lambda ,T]=1$, with $R_1$ calculated using Eq. (6).

Figure 4

(a) Ratio of the number of events and (b) probability of no events as a function of the recovery time $T$ for the real-time (open circles) and shuffled-time $*\to i$ (open squares) data with respect to the overall shuffled data. (c) Ratio of the average size of the outbreaks (open circles) and of $R_1$ calculated using Eq. (6) (dashed line).