Limit theorems for assortativity and clustering in null models for scale-free networks

Remco van der Hofstad, Pim Van der Hoorn*, Nelly Litvak, Clara Stegehuis

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is obtained when self-loops and multiple edges in the configuration model are removed. We prove an upper bound for the number of such erased edges for regularly-varying degree distributions with infinite variance, and use this result to prove central limit theorems for Pearson’s correlation coefficient and the clustering coefficient in the erased configuration model. Our results explain the structural correlations in the erased configuration model and show that removing edges leads to different scaling of the clustering coefficient. We prove that for the rank-1 inhomogeneous random graph, another null model that creates scale-free simple networks, the results for Pearson’s correlation coefficient as well as for the clustering coefficient are similar to the results for the erased configuration model.
Original languageEnglish
Pages (from-to)1035-1084
Number of pages50
JournalAdvances in applied probability
Volume52
Issue number4
DOIs
Publication statusPublished - 3 Dec 2020

Keywords

  • Degree–degree correlations
  • Clustering
  • Configuration model
  • Limit theorems

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