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Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data.

Alexander P Kartun-Giles¹, Dmitri Krioukov², James P Gleeson³

¹School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study introduces a new network model that is projective and generates sparse power-law networks. It addresses the challenge of reconciling network sparseness with projectivity and exchangeability in complex network science.

Keywords:

information theory of networks network entropy networks models projectivity and exchangeability

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Area of Science:

Network Science
Statistical Modeling
Complex Systems

Background:

Sparse complex network models are widely used but struggle to reconcile sparseness with projectivity and exchangeability.
Projective models allow predictions from subsamples, while exchangeable models are order-independent.
The interplay between network sparseness and these statistical properties remains an open scientific problem.

Purpose of the Study:

To propose a novel network process that is projective and generates sparse power-law networks.
To investigate the relationship between the proposed model and exchangeable networks.
To evaluate the utility of the proposed model as a null model for real-world network data.

Main Methods:

Development of a network process incorporating hidden variables.
Analysis of the model's properties regarding projectivity and exchangeability.
Information theory and network entropy characterization.
Testing the proposed network process as a null model on empirical data.

Main Results:

The proposed hidden variable network process is projective and generates sparse power-law networks.
The model, while not strictly exchangeable, shows a close relationship to exchangeable uncorrelated networks.
Empirical testing demonstrates the model's effectiveness as a null model for statistical network analysis.

Conclusions:

The proposed network process offers a viable solution for generating projective sparse power-law networks.
The model provides a valuable tool for statistical network modeling, particularly as a null model.
This work advances the understanding of reconciling network sparseness with key statistical properties in network science.