Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central limit theorems for local network statistics   Subgraph counts - in particular the number of occurrences of small shapes
such as triangles - characterize properties of random networks, and as a result
have seen wide use as network summary statistics. However, subgraphs are
typically counted globally, and existing approaches fail to describe
vertex-specific characteristics. On the other hand, rooted subgraph counts -
counts focusing on any given vertex's neighborhood - are fundamental
descriptors of local network properties. We derive the asymptotic joint
distribution of rooted subgraph counts in inhomogeneous random graphs, a model
which generalizes many popular statistical network models. This result enables
a shift in the statistical analysis of large graphs, from estimating network
summaries, to estimating models linking local network structure and
vertex-specific covariates. As an example, we consider a school friendship
network and show that local friendship patterns are significant predictors of
gender and race.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat