Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerating simple paths from connected induced subgraphs   We present an exact formula for the ordinary generating series of the simple
paths between any two vertices of a graph. Our formula involves the adjacency
matrix of the connected induced subgraphs and remains valid on weighted and
directed graphs. As a particular case, we obtain a relation linking the
Hamiltonian paths and cycles of a graph to its dominating connected sets.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom