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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.

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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.