# Blog Archives

## Cycle Detection in Graphs

In graph theory, the term **cycle** may refer to a closed 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**; see Cycle graph. 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…

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