Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Typical large graphs with given edge and triangle densities   The analysis of large simple graphs with extreme values of the densities of
edges and triangles has been extended to the statistical structure of typical
graphs of fixed intermediate densities, by the use of large deviations of
Erdoes-Renyi graphs. We prove that the typical graph exhibits sharp
singularities as the constraining densities vary between different curves of
extreme values, and we determine the precise nature of the singularities. The
extension to graphs with fixed densities of edges and k-cycles for odd k>3 is
straightforward and we note the simple changes in the proof.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con