Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Network modularity in the presence of covariates   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.

28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio