Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the density of triangles and squares in regular finite and unimodular
  random graphs   We explicitly describe the possible pairs of triangle and square densities
for r-regular finite simple graphs. We also prove that every r-regular
unimodular random graph can be approximated by r-regular finite graphs with
respect to these densities. As a corollary one gets an explicit description of
the possible pairs of the third and fourth moments of the spectral measure of
r-regular unimodular random graphs.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg