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* The [[Bellman–Ford algorithm]] can be used to detect a negative cycle in time <math>O(|V||E|)</math>.
* Cherkassky and Goldberg<ref>{{Cite journal |last1=Cherkassky |first1=Boris V. |last2=Goldberg |first2=Andrew V. |date=1999-06-01 |title=Negative-cycle detection algorithms |url=https://doi.org/10.1007/s101070050058 |journal=Mathematical Programming |language=en |volume=85 |issue=2 |pages=277–311 |doi=10.1007/s101070050058 |s2cid=79739 |issn=1436-4646|url-access=subscription }}</ref> survey several other algorithms for negative cycle detection.
==General algebraic framework on semirings: the algebraic path problem==
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