Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detailed balance = complex balance + cycle balance. A graph-theoretic
  proof for reaction networks and Markov chains   We further clarify the relation between detailed-balanced and
complex-balanced equilibria of reversible chemical reaction networks. Our
results hold for arbitrary kinetics and also for boundary equilibria. Detailed
balance, complex balance, "formal balance", and the new notion of "cycle
balance" are all defined in terms of the underlying graph. This fact allows
elementary graph-theoretic (non-algebraic) proofs of a previous result
(detailed balance = complex balance + formal balance), our main result
(detailed balance = complex balance + cycle balance), and a corresponding
result in the setting of continuous-time Markov chains.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org