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 opposite effects in information reach: 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 temporal patterns of human communication.Quantitative understanding of human communication patterns is of paramount importance to explain the dynamics of many social, technological and economic phenomena [1][2][3][4]. Most studies have focused on the study of the complex topological patterns of the underlying contact network (whom we talk to) and its influence in the properties of spreading phenomena in social networks such diffusion of information, innovations, computer viruses, opinions, etc. [2]. Paradoxically, most of these studies of dynamical phenomena on social networks neglect the temporal patterns of human communications: humans act in bursts or cascades of events [5][6][7][8], most ties are not persistent [9,10] and communications happen mostly in the form of group conversations [8,[11][12][13]. However, since information transmission and human communication are concurrent, the temporal structure of communication must influence the properties of information spreading. Indeed, recent experiments of electronic recommendation forwarding [14] and simulations of epidemic models on email and mobile databases [6,15] found that the asymptotic speed of information spreading is controlled by the bursty nature of human communications that leads to a slowing down of the diffusion. However, although the asymptotic speed is an important property of the propagation of information in social networks, there is still no general understanding of how and what temporal properties of human communication do influence spreading processes and in turn, how they affect the very definition of social interaction.The answer to this question can be framed in the more general problem of how to model dynamical social networks [9,16]. In most studies, real temporal activity is aggregated over time giving a static snapshot of the social interaction where ties are described by static strengths which do not include information about the temporal aspects of how humans interact. Temporal and topological aspects are therefore disentangled in the analysis. In this letter we merge both aspects in the case of information diffusion by adopting a functional definition of the social ties using the well-known map between dynamical epidemic models and static percolation [17]. The network is still described by a static graph, but the interaction strength between individuals now incorporates the causal and temporal patterns of their communications and not only on the intensity [18].To this end we study th...

Connectivity is the key process that characterizes the structural and functional properties of social networks. However, the bursty activity of dyadic interactions may hinder the discrimination of inactive ties from large interevent times in active ones. We develop a principled method to detect tie de-activation and apply it to a large longitudinal, cross-sectional communication dataset (≈19 months, ≈20 million people). Contrary to the perception of ever-growing connectivity, we observe that individuals exhibit a finite communication capacity, which limits the number of ties they can maintain active in time. On average men display higher capacity than women, and this capacity decreases for both genders over their lifespan. Separating communication capacity from activity reveals a diverse range of tie activation strategies, from stable to exploratory. This allows us to draw novel relationships between individual strategies for human interaction and the evolution of social networks at global scale.

We used a large database of 9 billion calls from 20 million mobile users to examine the relationships between aggregated time spent on the phone, personal network size, tie strength and the way in which users distributed their limited time across their network (disparity). Compared to those with smaller networks, those with large networks did not devote proportionally more time to communication and had on average weaker ties (as measured by time spent communicating). Further, there were not substantially different levels of disparity between individuals, in that mobile users tend to distribute their time very unevenly across their network, with a large proportion of calls going to a small number of individuals. Together, these results suggest that there are time constraints which limit tie strength in large personal networks, and that even high levels of mobile communication do not fundamentally alter the disparity of time allocation across networks. I. INTRODUCTIONDuring the last two decades the structural and the dynamic properties of social networks have been subject of intensive study (Watts,55). The structure of social networks is important not only from the perspective of the single user, but also from that of society as a whole, as it can influence various dynamic processes of human interaction, communication, spreading of information and disease transmission (Christakis and Fowler,11, Onnela et al.,38, Watts,55). Traditionally, these communication networks have been studied on a relatively small scale, using questionnaire or interview methods to gather data on how communication patterns are related to other characteristics such as social support (Wellman and Frank, 59) or the emotional intensity of the tie between two individuals (Roberts and Dunbar, 49). However, people's recollection of specific communication events is often imperfect (Bernard et al, 7) and the extent to which studies on specific, limited samples can be generalized to wider populations and countries is unclear (Henrich et al.,24, Wellman,57). With the rise of electronically-mediated communication, it is now becoming possible to study communication patterns in networks on a scale, and at a level of detail, not possible using traditional questionnaire or survey methods (Bohannon,10, Lazer et al.,29, Watts,56). Specifically in terms of mobile phone communication, access to data on this scale has led to advances in our understanding about the structure of mobile phone networks, network dynamics, factors influencing information transmission in the networks and reciprocity of communication (Miritello et al.,34, Onnela et al.,39, Palla et al.,42).One key variable that characterizes the structural topology of such networks is the social connectivity or degree of a node. It measures the number of people with whom an individual interacts and can also be interpreted as a measure of social integration (Marsden, 32) or activity (Wasserman et al.,54). In general, the degree distributions are skewed with a long tail, indicating that most users have on...

Social networks are made out of strong and weak ties having very different structural and dynamical properties. But what features of human interaction build a strong tie? Here we approach this question from a practical way by finding what are the properties of social interactions that make ties more persistent and thus stronger to maintain social interactions in the future. Using a large longitudinal mobile phone database we build a predictive model of tie persistence based on intensity, intimacy, structural and temporal patterns of social interaction. While our results confirm that structural (embeddedness) and intensity (number of calls) features are correlated with tie persistence, temporal features of communication events are better and more efficient predictors for tie persistence. Specifically, although communication within ties is always bursty we find that ties that are more bursty than the average are more likely to decay, signaling that tie strength is not only reflected in the intensity or topology of the network, but also on how individuals distribute time or attention across their relationships. We also found that stable relationships have and require a constant rhythm and if communication is halted for more than 8 times the previous communication frequency, most likely the tie will decay. Our results not only are important to understand the strength of social relationships but also to unveil the entanglement between the different temporal scales in networks, from microscopic tie burstiness and rhythm to macroscopic network evolution.

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong , the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the "edge of chaos" (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like attractors naturally emerge, consistently with recently proved generalizations of the CLT.

Recent research has shown the deep impact of the dynamics of human interactions (or temporal social networks) on the spreading of information, opinion formation, etc. In general, the bursty nature of human interactions lowers the interaction between people to the extent that both the speed and reach of information diffusion are diminished. Using a large database of 20 million users of mobile phone calls we show evidence this effect is not homogeneous in the social network but in fact, there is a large correlation between this effect and the social topological structure around a given individual. In particular, we show that social relations of hubs in a network are relatively weaker from the dynamical point than those that are poorer connected in the information diffusion process. Our results show the importance of the temporal patterns of communication when analyzing and modeling dynamical process on social networks.

PACS 05.45.Jn -High dimensional chaos PACS 05.45.Xt -Synchronization PACS 31.30-Jh -Long-range interactions PACS 05.70.Fh -Phase transitions in statistical mechanics and thermodynamicsAbstract. -We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-driven coupled pendula. We also show that, in the Kuramoto model, the shape of the phase transition and the largest Lyapunov exponent behavior are strongly dependent on the distribution of the natural frequencies.

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