Recent developments in sensing technologies have enabled us to examine the nature of human social behavior in greater detail. By applying an information-theoretic method to the spatiotemporal data of cellphone locations, [C. Song et al., Science 327, 1018(2010] found that human mobility patterns are remarkably predictable. Inspired by their work, we address a similar predictability question in a different kind of human social activity: conversation events. The predictability in the sequence of one's conversation partners is defined as the degree to which one's next conversation partner can be predicted given the current partner. We quantify this predictability by using the mutual information. We examine the predictability of conversation events for each individual using the longitudinal data of face-to-face interactions collected from two company offices in Japan. Each subject wears a name tag equipped with an infrared sensor node, and conversation events are marked when signals are exchanged between sensor nodes in close proximity. We find that the conversation events are predictable to a certain extent; knowing the current partner decreases the uncertainty about the next partner by 28.4% on average. Much of the predictability is explained by longtailed distributions of interevent intervals. However, a predictability also exists in the data, apart from the contribution of their long-tailed nature. In addition, an individual's predictability is correlated with the position of the individual in the static social network derived from the data. Individuals confined in a community-in the sense of an abundance of surrounding triangles-tend to have low predictability, and those bridging different communities tend to have high predictability.

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.

In many data sets, information on the structure and temporality of a system coexists with noise and non-essential elements. In networked systems for instance, some edges might be non-essential or exist only by chance. Filtering them out and extracting a set of relevant connections is a non-trivial task. Moreover, mehods put forward until now do not deal with time-resolved network data, which have become increasingly available. Here we develop a method for filtering temporal network data, by defining an adequate temporal null model that allows us to identify pairs of nodes having more interactions than expected given their activities: the significant ties. Moreover, our method can assign a significance to complex structures such as triads of simultaneous interactions, an impossible task for methods based on static representations. Our results hint at ways to represent temporal networks for use in data-driven models.

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.

Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for individuals are highly bursty. We examine some basic properties of event sequences generated by the Hawkes self-exciting process to show that it generates bursty interevent times for a wide parameter range. Then, we fit the model to the data of conversation sequences recorded in company offices in Japan. In this way, we can estimate relative magnitudes of the self excitement, its temporal decay, and the base event rate independent of the self excitation. These variables highly depend on individuals. We also point out that the Hawkes model has an important limitation that the correlation in the interevent times and the burstiness cannot be independently modulated.