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Studying Asymmetric Structure in Directed Networks by Overlapping and Non-Overlapping Models
1School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China.
Entropy (Basel, Switzerland)
|September 23, 2022
Summary
We introduce a new model for directed networks with asymmetric community structures, allowing overlapping sending and non-overlapping receiving clusters. This flexible model captures real-world network complexities and improves community detection accuracy.
Area of Science:
- Network Science
- Data Mining
- Statistical Modeling
Background:
- Existing models for directed networks often assume symmetrical community structures (either fully overlapping or non-overlapping).
- These models fail to capture real-world directed networks where sending communities may overlap while receiving communities do not, especially when the number of sending communities is limited.
- This limitation hinders accurate community detection in diverse real-world scenarios.
Purpose of the Study:
- To propose a novel model for directed networks that accommodates asymmetric community structures.
- To develop flexible and identifiable models for directed networks with overlapping sending and non-overlapping receiving clusters.
- To address the limitations of existing models in capturing specific real-world network properties.
Main Methods:
- Introduction of the Overlapping and Non-overlapping model (ONM) to handle asymmetric community structures.
- Development of an extended ONM variant to account for variations in node degree.
- Design and implementation of two spectral clustering algorithms tailored to fit the proposed ONM.
- Theoretical analysis to establish estimation consistency guarantees for the developed algorithms.
Main Results:
- The proposed ONM and its extension effectively model directed networks with asymmetric community properties.
- Spectral clustering algorithms demonstrate theoretical guarantees for estimation consistency.
- Simulations on computer-generated networks validate the theoretical findings.
- Analysis of real-world networks reveals the prevalence of highly mixed nodes and asymmetric structures.
Conclusions:
- The developed Overlapping and Non-overlapping model (ONM) provides a flexible framework for analyzing directed networks with asymmetric community structures.
- The proposed spectral clustering algorithms offer reliable methods for community detection in such networks.
- The findings highlight the importance of considering asymmetric structures for accurate network analysis in real-world applications.
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