cycle

In graph theory, a cycle is a specific type of path within a graph. A path is a sequence of vertices and edges, and a cycle is a closed path where the starting and ending vertices are the same, and no edges are repeated. For a path to be considered a cycle, it must have at least three vertices and the vertices (except for the start and end) must be distinct.

The concept of cycles is fundamental in graph theory, which itself is a branch of mathematics focused on networks of points (vertices) connected by lines (edges). This field has applications in various disciplines, including chemistry, computer science, and social sciences. An important related concept is an Eulerian cycle, which is a closed path that traverses every edge of a graph exactly once. The famous Königsberg bridge problem is a classic example that led to the development of Eulerian cycle theory.123