Feb 27, 2025 · What is Cycle? A cycle in graph is a closed path, meaning that it starts and ends at the same vertex while ensuring that no other vertices or edges are repeated. In other words, a cycle is formed by traversing a graph such that: No vertex is repeated, except for the starting and ending vertex, which must be the same and No edge is repeated.

Mar 13, 2023 · A cyclic graph is defined as a graph that contains at least one cycle which is a path that begins and ends at the same node, without passing through any other node twice.

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 without cycles is called an acyclic 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 n vertices is called Cn. [2] .

Mar 18, 2024 · A cycle consists of a sequence of adjacent and distinct nodes in a graph. The only exception is that the first and last nodes of the cycle sequence must be the same node. In this way, we can conclude that every cycle is a circuit, but the contrary is not true.

Apr 5, 2025 · To find cycle in a directed graph we can use the Depth First Traversal (DFS) technique. It is based on the idea that there is a cycle in a graph only if there is a back edge [i.e., a node points to one of its ancestors in a DFS tree] present in the graph.

Apr 30, 2025 · In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all nodes. A different sort of cycle graph, here termed a group cycle graph, is a graph which shows cycles of a group as well as the connectivity between the group cycles.

In the graph from Example 12.3.1, \((a, e, f, a)\) is a cycle of length \(3\), and \((b, g, d, h, c, f, b)\) is a cycle of length \(6\). Here are drawings of some small paths and cycles:

May 4, 2017 · A cycle is either: a simple graph (= no double edges, no loops) with 1 component and all vertices having vertex degree 2; a graph with 2 vertices and two edges between them; a graph with 1 vertex and a loop

A cycle in a Graph is a path that starts and ends at the same vertex, where no edges are repeated. It is similar to walking through a maze and ending up exactly where you started. A cycle can be defined slightly different depending on the situation.