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Cycle Detection in Graphs

Ravishing Journey

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 cyclecircuitcircle, 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 cycleintegral cycle, etc.
  • An edge set that has even degree at every vertex; also called an even edge set or…

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