Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf Algebras of Graphs   We define graded Hopf algebras with bases labeled by various types of graphs
and hypergraphs, provided with natural embeddings into an algebra of
polynomials in infinitely many variables. These algebras are graded by the
number of edges and can be considered as generalizations of symmetric or
quasi-symmetric functions.

6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin