Network modularity in the presence of covariates

Beate Ehrhardt, Patrick J. Wolfe

Research output: Contribution to journalReview articlepeer-review

3 Citations (SciVal)
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We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible null model. This provides for the first time an objective measure of whether or not a particular value of modularity is meaningful. In particular, our results quantify the strength of the relation between observed community structure and the interactions in a network. Our technical contribution is to provide limit theorems for modularity when a community assignment is given by nodal features or covariates. These theorems hold for a broad class of network models over a range of sparsity regimes, as well as for weighted, multiedge, and power-law networks. This allows us to assign $p$-values to observed community structure, which we validate using several benchmark examples from the literature. We conclude by applying this methodology to investigate a multiedge network of corporate email interactions.

Original languageEnglish
Pages (from-to)261-276
Number of pages16
JournalSiam Review
Issue number2
Early online date8 May 2019
Publication statusPublished - 2019


  • central limit theorems
  • degree-based network models
  • network community structure
  • nonparametric statistics
  • statistical network analysis
  • Network community structure
  • Limit theorems
  • Degree-based network models
  • Statistical network analysis

ASJC Scopus subject areas

  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics


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