Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for transition probabilities on graphs and isoperimetric
  inequalities   In this paper necessary and sufficient conditions are presented for heat
kernel upper bounds for random walks on weighted graphs. Several equivalent
conditions are given in the form of isoperimetric inequalities.

37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin