Abstract
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 language | English |
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Pages (from-to) | 261-276 |
Number of pages | 16 |
Journal | Siam Review |
Volume | 61 |
Issue number | 2 |
Early online date | 8 May 2019 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- 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