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Latent Poisson models for networks with heterogeneous density.

Tiago P Peixoto1

  • 1Department of Network and Data Science, Central European University, H-1051 Budapest, Hungary; ISI Foundation, Via Chisola 5, 10126 Torino, Italy; and Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom.

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Latent Poisson models reveal hidden multigraphs to capture network density heterogeneity. This approach improves community structure identification and disentangles correlations in sparse, real-world networks.

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Area of Science:

  • Network science
  • Statistical modeling
  • Graph theory

Background:

  • Empirical networks exhibit global sparsity but local density.
  • Understanding density heterogeneity is crucial for network analysis.
  • Existing models may struggle with mathematical tractability.

Purpose of the Study:

  • To introduce latent Poisson models for generating hidden multigraphs.
  • To capture density heterogeneity in empirical networks.
  • To improve upon existing methods for network analysis.

Main Methods:

  • Developing latent Poisson models for hidden multigraph generation.
  • Reconstructing latent multigraphs from simple graph data.
  • Analyzing degree-degree correlations and community structure.

Main Results:

  • Latent Poisson models effectively capture network density heterogeneity.
  • The proposed method is mathematically tractable.
  • Improved disentanglement of disassortative degree-degree correlations.
  • Enhanced identification of community structure in empirical networks.

Conclusions:

  • Latent Poisson models offer a powerful tool for analyzing complex network structures.
  • This approach provides new insights into network organization and community detection.
  • The method is applicable to empirically relevant network scenarios.