Fleury’s algorithm

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

1.

Pick any vertex to start
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.

Darken that edge, as a reminder that you can’t traverse it again
4.

Travel that edge, coming to the next vertex
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.