For example, Thomas H. Cormen, Charles E. Leiserson, Ronald Rivest, Clifford Stein. Introduction to Algorithms, problem 24-3 says:
Arbitrage is the use of discrepancies in currency exchange rates to transform one unit of a currency into more than one unit of the same currency. For example, suppose that 1 U.S. dollar buys 49 Indian rupees, 1 ...
I feel this is not a duplicate of a question asking about applications of graph theory as this goes the other way.
If you're talking purely about currency arbitrage, the quickest way seems to be finding a negative cycle in a graph of currency where the vertices are the currencies and the nodes the exchange rate.