Modern technologies not only provide a variety of communication modes (e.g., texting, cell phone conversation, and online instant messaging), but also detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study intercall duration of communications of the 100,000 most active cell phone users of a Chinese mobile phone operator. We confirm that the intercall durations follow a power-law distribution with an exponential cutoff at the population level but find differences when focusing on individual users. We apply statistical tests at the individual level and find that the intercall durations follow a power-law distribution for only 3,460 individuals (3.46%). The intercall durations for the majority (73.34%) follow a Weibull distribution. We quantify individual users using three measures: out-degree, percentage of outgoing calls, and communication diversity. We find that the cell phone users with a power-law duration distribution fall into three anomalous clusters: robot-based callers, telecom fraud, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operators in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cell phone users. We also discover more information about the calling patterns of these four clusters (e.g., the probability that a user will call the c r -th most contact and the probability distribution of burst sizes). Our findings may enable a more detailed analysis of the huge body of data contained in the logs of massive users.human dynamics | phone user categorization | social science | nonlinear dynamics | social networks U nderstanding the temporal patterns of individual human interactions is essential in managing information spreading and in tracking social contagion. Human interactions (e.g., cell phone conversations and e-mails) leave electronic traces that allow the tracking of human interactions from the perspective of either static complex networks (1-6) or human dynamics (7). Because static networks only describe sequences of instantaneous interacting links, temporal networks in which the temporal patterns of interacting activities for each node are recorded have recently received a considerable amount of research interest (8, 9). Investigations of interevent intervals between two consecutive interacting actions, such as e-mail communications (7, 10), shortmessage correspondences (11-13), cell phone conservations (14, 15), and letter correspondences (16-18), indicate that human interactions have non-Poissonian characteristics. Previous studies were conducted either on aggregate samples (14,15,19) or on a small group of selected individuals (7,(10)(11)(12)(16)(17)(18), but the communication behavior of individuals is not well understood.We study the complete voice information for cell phone users supplied by a Chinese cell phone operator and study the interevent time...

Big data open up unprecedented opportunities to investigate complex systems including the society. In particular, communication data serve as major sources for computational social sciences but they have to be cleaned and filtered as they may contain spurious information due to recording errors as well as interactions, like commercial and marketing activities, not directly related to the social network. The network constructed from communication data can only be considered as a proxy for the network of social relationships. Here we apply a systematic method, based on multiple hypothesis testing, to statistically validate the links and then construct the corresponding Bonferroni network, generalized to the directed case. We study two large datasets of mobile phone records, one from Europe and the other from China. For both datasets we compare the raw data networks with the corresponding Bonferroni networks and point out significant differences in the structures and in the basic network measures. We show evidence that the Bonferroni network provides a better proxy for the network of social interactions than the original one. By using the filtered networks we investigated the statistics and temporal evolution of small directed 3-motifs and conclude that closed communication triads have a formation time-scale, which is quite fast and typically intraday. We also find that open communication triads preferentially evolve to other open triads with a higher fraction of reciprocated calls. These stylized facts were observed for both datasets.

Mobile phone calling is one of the most widely used communication methods in modern society. The records of calls among mobile phone users provide us a valuable proxy for the understanding of human communication patterns embedded in social networks. Mobile phone users call each other forming a directed calling network. If only reciprocal calls are considered, we obtain an undirected mutual calling network. The preferential communication behavior between two connected users can be statistically tested and it results in two Bonferroni networks with statistically validated edges. We perform a comparative analysis of the statistical properties of these four networks, which are constructed from the calling records of more than nine million individuals in Shanghai over a period of 110 days. We find that these networks share many common structural properties and also exhibit idiosyncratic features when compared with previously studied large mobile calling networks. The empirical findings provide us an intriguing picture of a representative large social network that might shed new lights on the modelling of large social networks.

Much empirical evidence shows that individuals usually exhibit significant homophily in social networks. We demonstrate, however, skill complementarity enhances heterophily in the formation of collaboration networks, where people prefer to forge social ties with people who have professions different from their own. We construct a model to quantify the heterophily by assuming that individuals choose collaborators to maximize utility. Using a huge database of online societies, we find evidence of heterophily in collaboration networks. The results of model calibration confirm the presence of heterophily. Both empirical analysis and model calibration show that the heterophilous feature is persistent along the evolution of online societies. Furthermore, the degree of skill complementarity is positively correlated with their production output. Our work sheds new light on the scientific research utility of virtual worlds for studying human behaviors in complex socioeconomic systems.

Humans are heterogenous and the behaviors of individuals could be different from that at the population level. Such differences could originate from (1) different mechanisms governing individual activities, (2) the same mechanism but with different scales, or (3) both of them. We conduct an in-depth study of the temporal patterns of cellphone conversation activities of 73,339 anonymous cellphone users with the same truncated Weibull distribution of inter-call durations. We find that the individual call events exhibit a pattern of bursts, in which high activity periods are alternated with low activity periods. Surprisingly, the number of events in high activity periods are found to conform to a power-law distribution at the population level, but follow an exponential distribution at the individual level, which is a hallmark of the absence of memory in individual call activities. Such exponential distribution is also observed for the number of events in low activity periods. Together with the exponential distributions of inter-call durations within bursts and of the intervals between consecutive bursts, we demonstrate that the individual call activities are driven by two independent Poisson processes, which can be combined within a minimal model in terms of a two-state first-order Markov chain giving very good agreement with the empirical distributions using the parameters estimated from real data for about half of the individuals in our sample. By measuring directly the distributions of call rates across the population, which exhibit power-law tails, we explain the difference with previous population level studies, purporting the existence of power-law distributions, via the "Superposition of Distributions" mechanism: The superposition of many exponential distributions of activities with a power-law distribution of their characteristic scales leads to a power-law distribution of the activities at the population level. Our results and model provide a simple universal description of the diversity of individual behaviors avoiding the caveat of model misidentification resulting from the use of population level data. Our findings shed light on the origins of bursty patterns in other human activities.