2016/03/03 by Franke, Beate, Wolfe, Patrick J.
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1603.01214
We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric 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 weighted, multi-edge, and power-law networks. This allows us to assign p-values to observed community structure, which we validate using several benchmark examples in the literature. We conclude by applying this methodology to investigate a multi-edge network of corporate email interactions.