Directed cycle

A directed cycle is a closed sequence of directed edges whose orientations consistently lead back to the starting vertex. Its vertices are distinct except that the starting vertex is repeated at the end.

Directed graph: A graph whose edges have specified directions from one vertex to another. Directed cycles are closed routes formed from its oriented edges.
Reachability: The relation describing whether a path exists from one vertex to another in a graph. Following a directed cycle makes every vertex on it reachable from the others.
Dependency graph: A directed graph representing prerequisite or dependence relationships among objects. A directed cycle signals a circular dependency that may prevent orderly execution.
Undirected cycle: A closed sequence of edges in an undirected graph with no repeated vertices except the start and end. Unlike a directed cycle, it does not require every edge to point along the sequence.
Directed path: A sequence of directed edges in which each edge ends where the next begins. A directed cycle closes a directed path by returning to its start.
Cycle detection: The problem of determining whether a graph contains at least one cycle. Directed-cycle detection is a basic task in graph algorithms.
Deadlock: A state in which processes wait indefinitely for resources held by one another. A cycle in a resource-allocation graph can indicate deadlock when each resource has one instance.
Directed acyclic graph: A directed graph containing no directed cycles. It is the defining opposite condition to containing a directed cycle.
Vertex: A point in a graph that may be connected to other points by edges. A cycle visits vertices in sequence and repeats its starting vertex at the end.
Topological sorting: A linear ordering of vertices in a directed acyclic graph that respects every edge. A directed cycle makes such an ordering impossible.

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