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Summary
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This study introduces a flexible Bayesian approach to stochastic block models, allowing for adjustable node degree correction in network cluster analysis. Results show degree correction improves performance when degree heterogeneity exists, but is unnecessary otherwise.

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Area of Science:

  • Network Science
  • Statistical Modeling
  • Data Analysis

Background:

  • Stochastic block models (SBMs) are prominent for network cluster analysis, defining groups by link probabilities.
  • A Karrer-Newman extension introduced node degree correction for heterogeneity within groups, improving performance on some networks.
  • The necessity and appropriateness of degree correction in SBMs remain unclear.

Purpose of the Study:

  • To formulate the degree-corrected SBM as a nonparametric Bayesian model with an inferable degree correction parameter.
  • To develop principled methods for inferring the number of clusters and predicting missing links.
  • To evaluate the impact of degree correction on cluster recovery and link prediction.

Main Methods:

  • Developed a nonparametric Bayesian formulation of the degree-corrected stochastic block model.
  • Incorporated a parameter to control the degree of correction, allowing inference from data.
  • Utilized synthetic and real-world network data for model evaluation.

Main Results:

  • On synthetic data, degree correction improved cluster recovery and link prediction when degree heterogeneity was present.
  • Performance was comparable with or without degree correction when no within-cluster degree heterogeneity existed.
  • On real networks, predictive performance was similar, but degree correction sometimes led to fewer discovered clusters.

Conclusions:

  • The Bayesian framework offers a flexible approach to SBMs, enabling data-driven control of degree correction.
  • Degree correction is beneficial for networks with significant degree heterogeneity.
  • The model can simplify network structure by identifying more compact clusters of heterogeneous degree nodes.