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

Code:

//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

Code:

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?

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