Weibull Processes in Network Degree Distributions

2025-02-17

AI Summary

This study investigates the evolutionary patterns of degree distributions in large-scale collaborative networks—specifically the Microsoft Academic Graph and IMDb—to identify the optimal statistical model. Using large-scale temporal analysis and χ² goodness-of-fit tests, we systematically compare the Weibull, power-law, and log-normal distributions. Results show that the Weibull distribution significantly outperforms the other two models—improving goodness-of-fit by over 35%—particularly during network maturity. Key contributions include: (i) the first empirical validation that a Weibull process universally characterizes degree distribution evolution across heterogeneous collaborative domains; (ii) discovery of remarkable stability in the Weibull shape parameter *k* (0.8–1.0 for academic networks; 0.9–1.1 for entertainment networks), indicating constraint-driven growth as the dominant mechanism; and (iii) identification of novel phenomena such as flattening in the low-degree regime, challenging the conventional preferential attachment paradigm.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of 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 $2.72 imes 10^8$ and $1.88 imes 10^6$ 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.

Problem

• Analyzes degree distributions in large collaboration networks
• Compares Weibull, power-law, and log-normal distribution models
• Explores network evolution influenced by constraint-based growth

Innovation

• Weibull distributions fit degree distributions
• Shape parameters exhibit notable stability
• Collaboration network evolution influenced by constraints