Modern technologies not only provide a variety of communication modes, e.g., texting, cellphone conversation, and online instant messaging, but they also provide detailed electronic traces of these communications between individuals. These electronic traces indicate that the interactions occur in temporal bursts. Here, we study the inter-call durations of the 100,000 most-active cellphone users of a Chinese mobile phone operator. We confirm that the inter-call 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 inter-call durations follow a power-law distribution for only 3460 individuals (3.46%). The inter-call 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 cellphone users with a power-law duration distribution fall into three anomalous clusters: robotbased callers, telecom frauds, and telephone sales. This information is of interest to both academics and practitioners, mobile telecom operator in particular. In contrast, the individual users with a Weibull duration distribution form the fourth cluster of ordinary cellphone users. We also discover more information about the calling patterns of these four clusters, e.g., the probability that a user will call the cr-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. Understanding the temporal patterns of individual human interactions is essential in managing information spreading and in tracking social contagion. Human interactions, e.g., cellphone conversations and emails, 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 inter-event intervals between two consecutive interacting actions, such as email communications [7, 10] , short-message correspondences [11] [12] [13] , cellphone conservations [14, 15] , and letter correspondences [16] [17] [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 cellphone users supplied by a Chinese cellphone operator and study the inter-event time between two consecutive outgoing calls (inter-call duration). Our studies are performed at both the individual and group levels. To ensure better statistics, the top 100,000 cellphone users with the * zqjiang@ecust.edu.cn † wxzhou@ecust.edu.cn ‡ hes@bu.edu largest number of outgoing calls are chosen as our data sample, each having more than 997 outgoing calls. We propose a bottom-up approach to investigate individual cellphone communication dynamics: (1) finding the functional form of the distribution of each individual's intercall durations, (2) grouping individuals with the same distribution, and (3) understanding the calling patterns for each group. We apply an automatic fitting technology to each mobile phone user, and filter out two groups of users according to their inter-call duration distributions. One group is comprised of individuals with a power-law duration distribution (3,464 individuals) and the other is comprised of individuals with a Weibull duration distribution (73,339 individuals). We demonstrate that the two groups exhibit different calling patterns and that the individuals from the power-law group exhibit anomalous communication behaviors (e.g., the group includes individuals sending spam).
Also Jiang et al in REF have studied the temporal patterns of individual human interactions based on their calling data and the dynamics of calling patterns among cell phone users.
Calling patterns in human communication dynamics
PNAS 110: 1600-1605 (2013)
Computer Science Physics Medicine