Thread: All the paths between 2 nodes in a graph

I have a graph with not directed and which have cycles.
I need to find all the paths between 2 given nodes.

I've been able to write the code to find one path using BFS algorithm, but I can' modify it to make it return a list of all the paths.

This is my graph class

//unuseful methods omitted to shorten the code
public class Graph<V,E> {
 
    HashMap<Vertex<V>, List<Edge<V,E>>> graph;
 
    public Graph() {
        graph = new HashMap<Vertex<V>, List<Edge<V,E>>>();
    }
 
    /**
     * @return true if 2 nodes are adjacent
     */
    public boolean areAdjacent(Vertex<V> source, Vertex<V> destination)
 
    /**
     * @return all the edges in the graph
     */
    public Collection<Edge<V,E>> edges()
 
    /**
     * @return edge between 2 vertices
     */
    public Edge<V,E> getEdge(Vertex<V> source, Vertex<V> destination)
 
    /**
     * @return edges outgoing from source
     */
    public Collection<Edge<V,E>> outEdges(Vertex<V> source)
 
    /**
 
     * @return vertices reachable from source
     */
    public Collection<Vertex<V>> outVertices(Vertex<V> source)
 
    /**
     * @return all the vertices in the graph
     */
    public Collection<Vertex<V>> vertices()
}

This is the BFS function

public static List<Vertex<String>> bfs(Graph<String,Integer> g, Vertex<String> source, Vertex<String> destination) {
	Queue<Vertex<String>> queue = new ArrayDeque<Vertex<String>>();
	HashSet<Vertex<String>> marked = new HashSet<Vertex<String>>();
 
	List<Vertex<String>> path = new ArrayList<Vertex<String>>(); //will contain the vertices in the path found
 
	queue.add(source);
	marked.add(source);
	while(!queue.isEmpty()) {
		Vertex<String> u = queue.remove();
 
		path.add(u);
 
		if(u.equals(destination)) { break; }
 
		for(Vertex<String> v : g.outVertices(u)) {
			if(!marked.contains(v)) {
				queue.add(v);
				marked.add(v);
			}
		}
	}
	return path;
}

It returns the list of vertices conteined in the first path found.
How do I have to modify the BFS function to make it find all the paths between the 2 given vertices and return a list of all those paths?

Thanks to have heard to my request to reply by private message...

By the way I've solved by myself.