Calling patterns in human communication dynamics

Abstract

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...

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