Latent Poisson models for networks with heterogeneous density.

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.