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On Edge Exchangeable Random Graphs.

Svante Janson1

  • 1Department of Mathematics, Uppsala University, PO Box 480, 751 06 Uppsala, Sweden.

Journal of Statistical Physics
|April 2, 2019
PubMed
Summary
This summary is machine-generated.

This study explores a new random graph model, demonstrating its ability to generate diverse graph structures, including dense and sparse networks with power-law distributions.

Keywords:
Dense and sparse graph limitsEdge exchangeable random graphsGraphons

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Area of Science:

  • Graph theory
  • Probability theory
  • Network science

Background:

  • The Crane and Dempsey model for edge exchangeable random graphs offers a novel framework for generating random graph structures.
  • Understanding the asymptotic properties of these graphs is crucial for their application in various fields.

Purpose of the Study:

  • To investigate the asymptotic behaviors of random simple graphs generated by merging multiple edges within the Crane and Dempsey model.
  • To analyze the diversity of graph structures (dense, sparse, power-law distributions) produced by this model.

Main Methods:

  • Analysis of asymptotic properties of random graphs.
  • Examination of graph convergence using graph limit theory.
  • Construction and study of specific model examples to illustrate different behaviors.

Main Results:

  • The model can generate dense, sparse, and extremely sparse random graphs.
  • One example exhibits a power-law degree distribution.
  • Demonstrated convergence to graph limits in some cases, while other examples show convergence to generalized graphons.

Conclusions:

  • The Crane and Dempsey model is versatile, capable of producing a wide spectrum of random graph properties.
  • The model's flexibility allows for the generation of graphs with complex limiting behaviors, including non-integrable generalized graphons.