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:

• Cycle (graph theory), a cycle in a graph
• Forest (graph theory), an undirected graph with no cycles
• Biconnected graph, an undirected graph in which every edge belongs to a cycle
• Directed acyclic graph, a directed graph with no cycles
• Strongly connected graph, a directed graph in which every edge belongs to a cycle
• Aperiodic graph, a directed graph in which the cycle lengths have no nontrivial common divisor
• Pseudoforest, a directed or undirected graph in which every connected component includes at most one cycle
• Cycle graph, a graph that has the structure of a single cycle
• Pancyclic graph, a graph that has cycles of all possible lengths
• Cycle detection (graph theory), the algorithmic problem of finding cycles in graphs

Other similarly-named concepts include

• Cycle graph (algebra), a graph that illustrates the cyclic subgroups of a group
• Circulant graph, a graph with an automorphism which permutes its vertices cyclically.