**Cycle (graph Theory)**

In graph theory, the term **cycle** may refer one of two types of specific cycles: a closed walk or simple path. If repeated vertices are allowed, it is more often called a **closed walk**. If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a **simple cycle**, **circuit**, **circle**, or **polygon**. A cycle in a directed graph is called a directed cycle.

The term *cycle* may also refer to:

- An element of the binary or integral (or real, complex, etc.) cycle space of a graph. This is the usage closest to that in the rest of mathematics, in particular algebraic topology. Such a cycle may be called a binary cycle, integral cycle, etc.
- An edge set that has even degree at every vertex; also called an even edge set or, when taken together with its vertices, an even subgraph. This is equivalent to a binary cycle, since a binary cycle is the indicator function of an edge set of this type.

Chordless cycles in a graph are sometimes called graph holes. A graph antihole is the complement of a graph hole.

Read more about Cycle (graph Theory): Cycle Detection

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### Famous quotes containing the word cycle:

“The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a *cycle* transmission as he does at the top of a mountain or in the petals of a flower.”

—Robert M. Pirsig (b. 1928)