An **Eulerian cycle** (**Eulerian circuit**, **Euler tour**) in a graph is a cycle with uses each edge precisely once. If such cycle exists, the graph is called **Eulerian**.

The name is after a famous mathematician Leonhard Euler, who stated and solved the **problem of Seven Bridges of Königsberg** in 1736, which is the first formally discussed problem in graph theory.

L.Euler showed that an Eulerian cycle exists if and only if all vertices in the graph are of even degree. An Eulerian path exists, if and only if at most two vertices in the graph are of odd degree.