In mathematics, a cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. See:
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Cycle (graph theory)
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.
A graph wit ...
, a cycle in a graph
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Forest (graph theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by ''exactly one'' path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ...
, an undirected graph with no cycles
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Biconnected graph
In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected graph has no articulation vertices.
The property of being ...
, an undirected graph in which every edge belongs to a cycle
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Directed acyclic graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one v ...
, a directed graph with no cycles
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Strongly connected graph
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that ...
, a directed graph in which every edge belongs to a cycle
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Aperiodic graph
In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer ''k'' > 1 that divides the length of every cycle of the graph. Equivalently, a graph is aperiodic if the greatest common divisor of the leng ...
, a directed graph in which the cycle lengths have no nontrivial common divisor
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Pseudoforest
In graph theory, a pseudoforest is an undirected graphThe kind of undirected graph considered here is often called a multigraph or pseudograph, to distinguish it from a simple graph. in which every connected component has at most one cycle. Tha ...
, a directed or undirected graph in which every connected component includes at most one cycle
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Cycle graph
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if the graph is simple) connected in a closed chain. The cycle graph with vertices is called ...
, a graph that has the structure of a single cycle
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Pancyclic graph
In the mathematical study of graph theory, a pancyclic graph is a directed graph or undirected graph that contains cycles of all possible lengths from three up to the number of vertices in the graph.. Pancyclic graphs are a generalization of Hami ...
, a graph that has cycles of all possible lengths
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Cycle detection (graph theory)
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.
A graph witho ...
, the algorithmic problem of finding cycles in graphs
Other similarly-named concepts include
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Cycle graph (algebra)
In group theory, a subfield of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups.
A cycle is the set of powers of a given group eleme ...
, a graph that illustrates the cyclic subgroups of a group
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Circulant graph
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes called a cyclic graph, but this term has other meanings.
Equivalent definitions
Cir ...
, a graph with an
automorphism which permutes its vertices cyclically.
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