In this study we analyze the dynamics of the contact list evolution of millions of users of the Skype communication network. We find that egocentric networks evolve heterogeneously in time as events of edge additions and deletions of individuals are grouped in long bursty clusters, which are separated by long inactive periods. We classify users by their link creation dynamics and show that bursty peaks of contact additions are likely to appear shortly after user account creation. We also study possible relations between bursty contact addition activity and other user-initiated actions like free and paid service adoption events. We show that bursts of contact additions are associated with increases in activity and adoption—an observation that can inform the design of targeted marketing tactics.
What determines the timing of human actions? A big question, but the science of human dynamics is here to tackle it. And its predictions are of practical value: for example, when ISPs decide what bandwidth an institution needs, they use a model of the likely timing and activity level of the individuals. Current models assume that an individual has a well defined probability of engaging in a specific action at a given moment, but evidence that the timing of human actions does not follow this pattern (of Poisson statistics) is emerging. Instead the delay between two consecutive events is best described by a heavy-tailed (power law) distribution. Albert-Laszlo Barabasi proposes an explanation for the prevalence of this behaviour. The ‘bursty’ nature of human dynamics, he finds, is a fundamental consequence of decision making. We study the dynamic network of e-mail traffic and find that it develops self-organized coherent structures similar to those appearing in many nonlinear dynamic systems. Such structures are uncovered by a general information theoretic approach to dynamic networks based on the analysis of synchronization among trios of users. In the e-mail network, coherent structures arise from temporal correlations when users act in a synchronized manner. These temporally linked structures turn out to be functional, goal-oriented aggregates that must react in real time to changing objectives and challenges (e.g., committees at a university). In contrast, static structures turn out to be related to organizational units (e.g., departments). Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution for a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems. Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems. We investigate the communication sequences of millions of people through two different channels and analyse the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his her several neighbours, thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constraints (for short messages) and partly to the human behavioural features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics. The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intense activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. Here we propose to characterize the bursty nature of real signals using orthogonal measures quantifying two distinct mechanisms leading to burstiness: the interevent time distribution and the memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to the changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up avenues for future work. Copyright c �EPLA, 2008 Abstract Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time τ between consecutively sent e-mails decays asymptotically as τ−α, with α ≈ 1. The slower-than-exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading nonhomogeneous Poisson process that explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems. complex systems human activity hypothesis testing point process We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents’ behavior at short time scales in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group or vice versa. Different distributions of contact times and intercontact times between individuals are obtained by considering transition probabilities with memory effects, i.e., the transition probabilities for each agent depend both on its state isolated or interacting and on the time elapsed since the last change in state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended and paves the way for systematic investigations of dynamical processes occurring on rapidly The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as heavy tail behavior in the inter-event time distribution. As the cause of such a bursty behavior two main mechanisms have been suggested: (i) inhomogeneities due to the circadian and weekly activity patterns and (ii) inhomogeneities rooted in human task execution behavior. In this paper, we investigate the role of these mechanisms by developing and then applying systematic de-seasoning methods to remove the circadian and weekly patterns from the time series of mobile phone communication events of individuals. We find that the heavy tails in the inter-event time distributions remain robust with respect to this procedure, which clearly indicates that the human task execution-based mechanism is a possible cause of the remaining burstiness in temporal mobile phone communication patterns. The high level of dynamics in today's online social networks (OSNs) creates new challenges for their infrastructures and providers. In particular, dynamics involving edge creation has direct implications on strategies for resource allocation, data partitioning and replication. Understanding network dynamics in the context of physical time is a critical first step towards a predictive approach towards infrastructure management in OSNs. Despite increasing efforts to study social network dynamics, current analyses mainly focus on change over time of static metrics computed on snapshots of social graphs. The limited prior work models network dynamics with respect to a logical clock. In this paper, we present results of analyzing a large timestamped dataset describing the initial growth and evolution of a large social network in China. We analyze and model the burstiness of link creation process, using the second derivative, i.e. the acceleration of the degree. This allows us to detect bursts, and to characterize the social activity of a OSN user as one of four phases: acceleration at the beginning of an activity burst, where link creation rate is increasing; deceleration when burst is ending and link creation process is slowing; cruising, when node activity is in a steady state, and complete inactivity.