Cycle Detection
An undirected graph has a cycle if and only if a depth-first search (DFS) finds an edge that points to an already-visited vertex (a back edge). Equivalently, all the back edges, which DFS skips over, are part of cycles. In the case of undirected graphs, only O(n) time is required, since at most n − 1 edges can be tree edges (where n is the number of vertices).
A directed graph has a cycle if and only if a DFS finds a back edge. Forward and cross edges do not necessarily indicate cycles. Many topological sorting algorithms will detect cycles too, since those are obstacles for topological order to exist. Also, if a directed graph has been divided into strongly connected components, cycles only exist within the components and not between them, since cycles are strongly connected.
Applications of cycle detection include the use of wait-for graphs to detect deadlocks in concurrent systems.
Read more about this topic: Cycle (graph Theory)
Famous quotes containing the word cycle:
“The cycle of the machine is now coming to an end. Man has learned much in the hard discipline and the shrewd, unflinching grasp of practical possibilities that the machine has provided in the last three centuries: but we can no more continue to live in the world of the machine than we could live successfully on the barren surface of the moon.”
—Lewis Mumford (1895–1990)