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 witho ...
, 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 ''a ...
, 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 ve ...
, 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 ...
, 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 len ...
, 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 Cycle (graph theory), cycles of all possible lengths from three up to the number of vertex (graph theory), vertices in the graph.. Pa ...
, 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 elemen ...
, 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
Circ ...
, a graph with an
automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms ...
which permutes its vertices cyclically.
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