Statistical models for cores decomposition of an undirected random graph

@article{Karwa2014StatisticalMF,
  title={Statistical models for cores decomposition of an undirected random graph},
  author={Vishesh Karwa and Michael J. Pelsmajer and Sonja Petrovic and Despina Stasi and Dane Wilburne},
  journal={ArXiv},
  year={2014},
  volume={abs/1410.7357}
}
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core decomposition as a tool to model random graphs. We propose using the shell distribution vector, a way of summarizing the decomposition, as a sufficient statistic for a family of exponential random graph models. We study the properties and behavior of the model… Expand
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