Fleury's algorithm is very important in allowing us to be able to construct an Eulerian trail given an Eulerian graph $G$. We briefly describe this algorithm below.
Steps to Fleury's Algorithm
|Step 1||Select any vertex to start with.|
|Step 2||Traverse any available edge starting with this vertex. Only traverse a bridge if there is no alternative edge to select.|
|Step 3||Repeat step 2 until there are no more edges left. The resulting trail will be an Eulerian trail (given an Eulerian graph).|