Source-linked AI summary
Calling patterns in human communication dynamics
Zhi-Qiang Jiang, Wen-Jie Xie, Ming-Xia Li, Boris Podobnik, Wei-Xing Zhou, H. Eugene Stanley
TL;DR
The paper examines how population-level calling patterns relate to heterogeneous individual behaviors. It classifies individual inter-call durations and callers, finding that most callers follow Weibull distributions while a small anomalous group follows power laws.
Problem
Population-level calling durations can obscure the heterogeneous behaviors of individual callers.
Method
The study defines intraday inter-call durations, applies statistical distribution tests, and groups callers using out-degree and communication diversity.
Results
3.46% of callers have power-law inter-call durations, while 73.34% follow Weibull distributions; the power-law group forms three anomalous clusters.
Takeaways & Limitations
Models of cellphone usage should represent heterogeneous individuals through clusters rather than assuming identical behavior.
Abstract
from arXiv · showhide
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.
Calling Patterns in Human Communication Dynamics
The study analyzes inter-call durations across cellphone users at population and individual levels, revealing that aggregate power-law behavior masks heterogeneous individual distributions. Users with power-law durations form three anomalous calling clusters, whereas Weibull users form one ordinary cluster.
- Calling Patterns in Human Communication Dynamics: The study analyzes outgoing-call inter-event durations in cellphone records at both individual and group levels.It uses a bottom-up approach that fits each user’s duration distribution, groups users by distribution, and then analyzes group calling patterns.
- Calling Patterns in Human Communication Dynamics: Individual power-law exponents average ⟨γ⟩ = 2.00 ± 0.32, contrasting with aggregate exponents below 1.None of the individual power-law exponents is below 1.5, whereas aggregate exponents include γ = 1.69 for the power-law group and values below 1 across outgoing-call groups.
- Calling Patterns in Human Communication Dynamics: Power-law users form three clusters with extreme calling patterns, while Weibull users form a single ordinary cluster.The three power-law clusters are distinguished using out-degree, outgoing-call percentage, and communication diversity; their average degrees are 21.76, 114.98, and 2083.3.
Discussion
Individual calling behavior is heterogeneous: most callers have Weibull inter-call durations, while a small power-law group shows anomalous patterns. The study uses distribution-based classification and cluster analysis to support individual-level modeling of cellphone activity.
- 3.46% of callers have power-law inter-call durations, while 73.34% have Weibull durations.
- Power-law callers exhibit anomalous patterns associated with robot-based calls, telecom frauds, and telephone sales.
- The population-level power law with exponential cutoff coexists with predominantly Weibull individual distributions, reflecting heterogeneous calling behaviors.
- Cluster-based modeling treats callers as heterogeneous groups whose similarities can support dynamic models of individual activity.
- Intraday inter-call durations are measured between consecutive calls within one-day periods separated at 4:00 A.M. to limit discontinuous-day effects.
- The study classifies individuals by inter-call-duration distributions and applies maximum-likelihood fits and Kolmogorov-Smirnov tests to truncated durations.