School of Business, East China University of Science and Technology, Shanghai 200237, China.
Proc Natl Acad Sci U S A. 2013 Jan 29;110(5):1600-5. doi: 10.1073/pnas.1220433110. Epub 2013 Jan 14.
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.
现代技术不仅提供了多种通信模式（例如短信、手机通话和在线即时消息），还为这些个人之间的通信提供了详细的电子痕迹。这些电子痕迹表明，交互是在时间上爆发的。在这里，我们研究了中国一家移动电话运营商的 10 万名最活跃的手机用户之间的通话持续时间。我们确认通话持续时间在人群水平上遵循幂律分布，并且在关注个人用户时存在差异。我们在个人水平上应用统计检验，发现只有 3460 个人（3.46%）的通话持续时间遵循幂律分布。大多数人的通话持续时间（73.34%）遵循威布尔分布。我们使用三个指标对个人用户进行量化：出度、外出电话的百分比和通信多样性。我们发现，具有幂律持续时间分布的手机用户分为三个异常集群：基于机器人的呼叫者、电信欺诈和电话销售。这一信息对学术界和从业者都有兴趣，特别是移动电信运营商。相比之下，具有威布尔持续时间分布的个人用户形成了第四组普通手机用户集群。我们还发现了有关这四个集群呼叫模式的更多信息（例如，用户将呼叫第 c(r)个联系人的概率以及突发大小的概率分布）。我们的研究结果可能会实现对大量用户日志中包含的大量数据的更详细分析。
