Fleury's Algorithm is a graph traversal algorithm used to find the next edge in an Eulerian path or circuit. Its purpose is to find the next edge that can be traversed without repeating any edges in a graph.
Fleury's Algorithm works by starting at a given vertex and traversing to a neighboring vertex, removing the edge that was traversed. It continues this process until all edges have been traversed, creating an Eulerian path or circuit.
An Eulerian path is a path in a graph that visits every edge exactly once, while an Eulerian circuit is a path that starts and ends at the same vertex, visiting every edge exactly once.
Fleury's Algorithm is used when trying to find a path or circuit that visits every edge in a graph exactly once, such as in the Seven Bridges of Königsberg problem.
The advantages of Fleury's Algorithm include its simplicity and efficiency for finding Eulerian paths and circuits. However, it can only be used on undirected graphs and can get stuck in a loop if there are multiple possible paths to take at a given vertex.