Weibull Processes in Network Degree Distributions

TL;DR

This paper demonstrates that Weibull distributions more accurately model degree distributions in large collaboration networks than traditional power-law or log-normal models, especially as networks mature, indicating constraint-based growth influences.

Contribution

It provides empirical evidence that Weibull distributions fit network degree data better than traditional models and reveals stable shape parameters over network evolution.

Findings

Weibull fits outperform power-law and log-normal models.

Stable Weibull shape parameters observed across network growth.

Degree distributions show characteristic flattening in mature networks.

Abstract

This study examines degree distributions in two large collaboration networks: the Microsoft Academic Graph (1800-2020) and Internet Movie Database (1900-2020), comprising $2.72 \times 10^8$ and $1.88 \times 10^6$ nodes respectively. Statistical comparison using $\chi^2$ measures showed that Weibull distributions fit the degree distributions better than power-law or log-normal models, especially at later stages in the network evolution. The Weibull shape parameters exhibit notable stability ($k \approx 0.8$-$1.0$ for academic, $k \approx 0.9$-$1.1$ for entertainment collaborations) despite orders of magnitude growth in network size. While early-stage networks display approximate power-law scaling, mature networks develop characteristic flattening in the low-degree region that Weibull distributions appear to capture better. In the academic network, the cutoff between the flattened region and power-law tail shows a gradual increase from $5$ to $9$ edges over time, while the entertainment network maintains a distinctive degree structure that may reflect storytelling and cast-size constraints. These patterns suggest the possibility that collaboration network evolution might be influenced more by constraint-based growth than by pure preferential attachment or multiplicative processes.