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Ordered community detection in directed networks.

Tiago P Peixoto¹

¹Department of Network and Data Science, Central European University, 1100 Vienna, Austria.

Physical Review. E

|September 16, 2022

Summary

This summary is machine-generated.

We introduce a new Bayesian method to uncover ordered community structures in directed networks. This approach effectively identifies hierarchical relationships and distinguishes them from simple degree imbalances.

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Area of Science:

Network science
Statistical modeling
Computational social science

Background:

Inferring community structure is crucial for understanding complex systems.
Directed networks often exhibit hierarchical organization, but existing methods struggle to capture this.
Distinguishing true hierarchical structure from local degree imbalances remains a challenge.

Purpose of the Study:

To develop a novel nonparametric Bayesian method for inferring ordered community structure in directed networks.
To incorporate latent one-dimensional hierarchies that dictate preferred edge direction.
To differentiate hierarchical organization from local degree imbalances.

Main Methods:

Modification of the stochastic block model (SBM) using a nonparametric Bayesian approach.
Leveraging rank alignment and coherence for parsimonious network descriptions.
Incorporating directed degree correction to resolve conflation with local degree imbalances.
Comparison with unordered SBM variants to assess statistical significance of hierarchy.

Main Results:

The proposed method successfully infers community structure with latent hierarchical ordering.
The model effectively distinguishes nonlocal hierarchical structure from local degree imbalances.
Demonstrated ability to determine if hierarchical ordering is statistically warranted.
Successful application across diverse empirical networks.

Conclusions:

The developed method provides a robust framework for analyzing hierarchical community structures in directed networks.
This approach enhances the understanding of network organization by separating global hierarchy from local properties.
The method offers a statistically sound way to validate the presence of hierarchical structures.