How to make graph traversal algorithm to work with large graph?

I am writing an algorithm to traverse through the graph when given a source and destination. The algorithm should traverse and show all possible paths from source to destination in the graph. I am using Breadth First Search to do this and it worked in small graph. But when a huge graph is supplied (having more than 1000 vertex), the program seems to be freezed and does not show any output after a long time. May I know how to solve this?

A simple one test that I have conducted (small graph)

    graph.addVertex("A", 25);
graph.addVertex("B", 60);
graph.addVertex("C", 45);
graph.addVertex("D", 75);
graph.addVertex("E", 95);
graph.addVertex("F", 85);
graph.addVertex("G", 105);
graph.addEdge("A", "B", "AB", "");
graph.addEdge("A", "D", "AD", "");
graph.addEdge("A", "C", "AC", "");
graph.addEdge("A", "E", "AE", "");
graph.addEdge("B", "E", "BE", "");
graph.addEdge("E", "F", "EF", "");
graph.addEdge("E", "G", "EG", "");
graph.addEdge("D", "C", "DC", "");
graph.addEdge("D", "F", "DF", "");
graph.addEdge("F", "G", "FG", "");
graph.addEdge("C", "F", "CF", ""); 
String str = graph.bfs("A", "G");
System.out.println(str);

My Breadth First Search Algorithm

// SUBMODULE: bfs
// IMPORT: src (String), dest (String)
// EXPORT: T (String) 
public String bfs( String src, String dest )
{
String T = "";
DSAQueue Q = new DSAQueue();             // The queue will store linked list
DSALinkedList path = null;                   // This is the list for queue
DSALinkedList adj = null;                    // Adjacency for src
adj = getAdjacent( src );
// Make adjacent to linked list first and store in queue
for( Object o : adj )
{
DSALinkedList ll = new DSALinkedList(); // Creating list for every iteration
DSAGraphVertex vertex = (DSAGraphVertex) o;
ll.insertLast( vertex );                // Every adjacent vertex is ele of list 
Q.enqueue( ll );                        // Store the list to queue
}
// ASSERTION: We Iterate until Q is empty, Q will store all L[V]
while( !Q.isEmpty() )
{
path = (DSALinkedList) Q.dequeue();          // Dequeue a linked list
// Get the tail of list
DSAGraphVertex v = (DSAGraphVertex) path.peekLast(); 
// We found the complete list path when the tail is dest
if( v.getLabel().equals(dest) )
{
T += src + " -> ";
for( Object o : path )
{
DSAGraphVertex pathVertex = (DSAGraphVertex) o;
T += pathVertex.getLabel() + " -> ";
}
T += "(END)\n";
}
else
{
// If v.getLabel() is not dest, we need to do bfs from adj of tail
DSALinkedList tailAdj = v.getAdjacent();
// Check the number of paths in this vertex
if( v.getSize() == 1 ) 
{
/* If only one path found, simply traverse to the only one path */
DSAGraphVertex headVertex = (DSAGraphVertex) tailAdj.peekFirst();    // head of the tailAdj
path.insertLast( headVertex );                  
Q.enqueue( path );
headVertex = null;
}
else
{
/* If the vertex has more than one path, copy all the existing paths for 
every single connection, then insert the new node to each list */
for( Object o : tailAdj )
{
DSALinkedList newList = new DSALinkedList();
newList = copyList( path );                 // Copy the existing
// Then add the new node into the copied list
DSAGraphVertex currVertex = (DSAGraphVertex) o; 
newList.insertLast( currVertex );
// The queue now has a new list of paths 
Q.enqueue( newList );       
newList = null;
}
}
tailAdj = null;
}
path = null;
}
return T;
}

1000 nodes isn't that big of a graph. I imagine you have an infinite loop somewhere in your code. Let's see here you have one possible place for an infinite loop: while( !Q.isEmpty() )

Ah yes, I don't see anything that stops you from adding nodes to the queue. The queue should only process each node once. You need to keep a list of nodes that have been added to the queue and are not allowed to be added again.

It doesn't stop quickly, because you never stop adding stuff to the queue, so it can never be empty.

Your lesson of the day: Whenever you have a loop that only ends when a condition is met, make doubly sure it's possible for that condition to be met.