Ehrhardt, B;
Wolfe, PJ;
(2019)
Network Modularity in the Presence of Covariates.
SIAM Review
, 61
(2)
pp. 261-276.
10.1137/17M1111528.
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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.
| Type: | Article |
|---|---|
| Title: | Network Modularity in the Presence of Covariates |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/17M1111528 |
| Publisher version: | https://doi.org/10.1137/17M1111528 |
| Language: | English |
| Additional information: | Copyright © 2019 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license (http://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10089119 |
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