Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elementary proof of Rayleigh formula for graphs   The Rayleigh monotonicity is a principle from the theory of electrical
networks. Its combinatorial interpretation says for each two edges of a graph
G, that the presence of one of them in a random spanning tree of G is
negatively correlated with the presence of the other edge. In this paper we
give a self-contained (inductive) proof of Rayleigh monotonicity for graphs.

32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int