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PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks.

Thong Pham¹, Paul Sheridan², Hidetoshi Shimodaira¹

¹Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Osaka, Japan.

|September 18, 2015

Summary

We developed PAFit, a new method to measure preferential attachment in complex networks. PAFit accurately estimates network growth patterns without assuming a specific form, outperforming older methods and revealing deviations from common models.

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Area of Science:

Network science
Statistical modeling
Complex systems analysis

Background:

Preferential attachment is a key stochastic process explaining complex network topology.
Understanding its functional form is crucial for both theoretical and practical insights into real-world networks.

Purpose of the Study:

To introduce PAFit, a novel maximum likelihood-based estimation method for measuring preferential attachment in temporal complex networks.
To provide a nonparametric framework for attachment kernel estimation, free from assumptions on its functional form.

Main Methods:

Developed PAFit, a maximum likelihood estimation method implemented as an R package.
Utilized a nonparametric statistical framework for attachment kernel estimation.
Performed Monte Carlo simulations to compare PAFit against existing methods (Jeong and Newman).

Main Results:

PAFit demonstrated superior performance over popular methods in Monte Carlo simulations.
Application to a Flickr social network dataset revealed deviations from the assumed log-linear attachment kernel form.
Identified and corrected a long-standing error in Newman's original preferential attachment method.

Conclusions:

PAFit offers a more accurate and flexible approach to measuring preferential attachment in temporal networks.
The findings challenge the universality of the log-linear model for attachment kernels in social networks.
The study contributes a corrected method and a robust tool for network science research.