(definition)
Definition: A path that starts and ends at the same vertex and includes at least one edge.
Generalization (I am a kind of ...)
path.
Specialization (... is a kind of me.)
Hamiltonian cycle, Euler cycle.
Aggregate parent (I am a part of or used in ...)
graph.
See also circuit (2).
Note: Also known as "circuit" or "closed path".
A cycle includes vertices other than the start/end at most once.
Having at least one edge means that there are at least two vertices in the path: the start/end and one other. It also means the path length is at least one.
One way to find a cycle is to do a depth-first search, checking for repeated vertices. One step in finding all cycles is to look for strongly connected components.
Author: PEB
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 15 October 2021.
HTML page formatted Fri Oct 15 16:48:46 2021.
Cite this as:
Paul E. Black, "cycle", in
Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 15 October 2021. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/cycle.html