def min_num_edges_between_nodes(graph,start_node):
    distance = 0
    shortest_path = []
    queue = [start_node] #FIFO
    levels = {}
    levels[start_node] = 0
    shortest_paths = {}
    shortest_paths[start_node] = ":"
    visited = [start_node]
    while len(queue)!=0:
        start = queue.pop(0)
        neighbours = graph[start]
        for neighbour,_ in neighbours.iteritems():
            if neighbour not in visited:
                queue.append(neighbour)
                visited.append(neighbour)
                levels[neighbour] = levels[start]+1
                shortest_paths[neighbour] = shortest_paths[start] +"->"+ start
    return levels, shortest_paths