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A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks
Hohyun Jung1,2, Frederick Kin Hing Phoa1
1Institute of Statistical Science, Academia Sinica, Taipei City 11529, Taiwan.
Entropy (Basel, Switzerland)
|April 30, 2021
Summary
This study introduces a new finite mixture model using truncated zeta distributions to accurately analyze network degree distributions, especially for small degrees where power-laws deviate. The model improves network analysis by handling discrete values and outperforming existing methods.
Area of Science:
- Network Science
- Complex Systems
- Data Analysis
Background:
- Degree distribution is crucial for understanding network topology.
- Real networks often exhibit power-law distributions, but deviate at small degrees.
- Continuous power-law models are inaccurate for discrete degree values.
Purpose of the Study:
- To propose a novel finite mixture model for network degree distributions.
- To address deviations from power-law behavior at small degrees.
- To accurately model discrete degree values in networks.
Main Methods:
- Developed a finite mixture model of truncated zeta distributions.
- Employed maximum likelihood estimation for parameter estimation.
- Utilized a model selection method to determine the number of mixture components.
- Validated the approach using Monte Carlo simulations.
Main Results:
- The proposed model effectively captures scale-free behavior while accounting for deviations at small degrees.
- Maximum likelihood and model selection methods accurately estimate parameters and components.
- Monte Carlo simulations confirm the algorithm's validity.
- The model demonstrates superior goodness-of-fit compared to alternatives.
Conclusions:
- The finite mixture model of truncated zeta distributions offers a more accurate representation of network degree distributions.
- This method enhances the analysis of complex networks, particularly those with scale-free properties and small-degree deviations.
- The approach provides valuable insights into the topological structure of scientific collaboration networks.
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