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Local dependence in random graph models: characterization, properties and statistical inference.

Michael Schweinberger1, Mark S Handcock2

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This summary is machine-generated.

This study introduces local dependence into random graph models, enabling statistical inference for relational data. This approach addresses limitations of conventional models, offering a more robust framework for analyzing complex networks.

Keywords:
Exponential familiesLocal dependenceM-dependenceModel degeneracySocial networksWeak dependence

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Area of Science:

  • Network science
  • Statistical modeling
  • Graph theory

Background:

  • Relational phenomena often lack clear neighborhood structures, unlike spatial or temporal ones.
  • Conventional exponential family random graph models struggle with statistical inference due to strong dependence and lack of local dependence characterization.

Purpose of the Study:

  • To characterize local dependence in random graph models.
  • To develop random graph models amenable to statistical inference for relational data.
  • To address the challenge of unknown neighborhood structures in relational networks.

Main Methods:

  • Inspired by spatial statistics and time series M-dependence to define finite neighborhoods.
  • Developed random graph models with local dependence.
  • Utilized Bayesian approaches to handle uncertainty in neighborhood structures.

Main Results:

  • Demonstrated that local dependence in random graph models leads to desirable properties for statistical inference.
  • Showcased that these models satisfy a crucial domain consistency condition, unlike conventional models.
  • Established a central limit theorem for random graph models with local dependence, supporting their inferential capabilities.

Conclusions:

  • Local dependence is key to making random graph models statistically tractable for relational data.
  • The proposed models offer a framework for analyzing networks with inherent local dependencies, even without predefined neighborhood structures.
  • The approach is validated through simulations and real-world network applications.