Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Distribution of the Number of Copies of Weakly Connected Digraphs
  in Random $k$NN Digraphs   In a digraph with $n$ vertices, a minuscule construct is a subdigraph with
$m<<n$ vertices. We study the number of copies of a minuscule constructs in $k$
nearest neighbor ($k$NN) digraph of the data from a random point process in
$\mathbb{R}^d$. Based on the asymptotic theory for functionals of point sets
under homogeneous Poisson process and binomial point process, we provide a
general result for the asymptotic behavior of the number of minuscule
constructs and as corollaries, we obtain asymptotic results for the number of
vertices with fixed indegree, the number of shared $k$NN pairs and the number
of reflexive $k$NN's in a $k$NN digraph.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat