Fleury’s algorithm constructs an Euler circuit in a graph (if it’s possible).

1. 1.

   Pick any vertex to start

2. 2.

   From that vertex pick an edge to traverse, considering following rule: never cross a bridge of the reduced graph unless there is no other choice

3. 3.

   Darken that edge, as a reminder that you can’t traverse it again

4. 4.

   Travel that edge, coming to the next vertex

5. 5.

   Repeat 2-4 until all edges have been traversed, and you are back at the starting vertex

By “reduced graph” we mean the original graph minus the darkened (already used) edges.