Fleury's Algorithm

Fleury's algorithm is an older method for finding an Eulerian circuit or Eulerian path in a graph by walking across edges one at a time and removing each edge once it has been used. At every step the algorithm avoids crossing a bridge, an edge whose removal would disconnect the remaining unused portion of the graph, unless crossing a bridge is the only option left at the current vertex, since burning a bridge too early can strand unused edges in a piece of the graph the walk can no longer reach. Fleury described the technique in 1883. Because checking whether an edge is currently a bridge takes real work and that check must be repeated at every step of the walk, the algorithm runs in time proportional to the square of the number of edges in the graph, considerably slower in the worst case than the linear-time Hierholzer's algorithm that is generally preferred today.