Calling patterns in human communication dynamics

TL;DR

This study analyzes cellphone call patterns, revealing that most users' inter-call durations follow a Weibull distribution, while a small subset exhibit power-law behavior linked to specific user types like frauds and sales, providing insights into communication dynamics.

Contribution

The paper identifies distinct statistical distributions of inter-call durations at the individual level and classifies users into clusters based on their calling patterns, highlighting anomalies such as fraud and sales activities.

Findings

Most users follow Weibull distribution in call durations.

A small subset (3.46%) follow power-law distributions linked to anomalies.

Distinct calling pattern clusters correlate with user types like frauds and sales.

Abstract

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: robot-based 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 $c_r$-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.