# Eulerian path

An **Eulerian path** is a path that traverses every edge only once in a graph. Being a path, it does not have to return to the starting vertex.

Let's look at the below graph.

graph {
  X -- Y;
  Y -- Z;
  X -- Z;
  Y -- O;
  Z -- O;
}
        

There are multiple Eulerian paths in the above graph. One such Eulerian path is `ZXYOZY`.

digraph g {
    bgcolor="transparent"
    Z -> X[label="1",weight="1"];
    X -> Y[label="2",weight="2"];
    Y -> O[label="3",weight="3"];
    O -> Z[label="4",weight="4"];
    Z -> Y[label="5",weight="5"];
}

# Eulerian circuit

An **Eulerian circuit** is a circuit that traverses every edge only once in a graph. Being a circuit, the starting and ending node of the traversal should be the same.

Let's look at the below graph.

graph g {
    bgcolor="transparent"
    B -- C
    B -- D
    C -- D
    A -- B
    A -- D
    B -- E
    E -- D
}

There are multiple Eulerian circuits in the above graph. One such Eulerian circuit is `BCDBEDAB`.

digraph g {
    bgcolor="transparent"
    B -> C[label="1"];
    C -> D[label="2"];
    D -> B[label="3"];
    B -> E[label="4"];
    E -> D[label="5"];
    D -> A[label="6"];
    A -> B[label="7"];
}

What are the Eulerian path and circuit in a graph?

Eulerian path An Eulerian path is a path that traverses every edge only once in a graph. Being a path, it does not have to return to the starting vertex. Let s look at the below graph. 