grapy.py

START, END  = 'A', 'E'
COORDINATE  = {
        'A' : [0,0],
        'B' : [2,0],
        'C' : [0,5],
        'D' : [4,1],
        'E' : [4,0]
    }
EDGE        = {
        'A' : ['B','C','D'],
        'B' : ['D','E','A'],
        'C' : ['B','A'],
        'D' : ['B','A'],
        'E' : ['B']
    }

def distance(node_1, node_2):
    if node_2 in EDGE[node_1]:
        x1, y1 = COORDINATE[node_1]
        x2, y2 = COORDINATE[node_2]
        return ( ((x1-x2)**2) + ((y1-y2)**2) ) ** 0.5
    else:
        return -1

def path_distance(nodes):
    total = 0
    for i in range(len(nodes)-1):
        dist = distance(nodes[i],nodes[i+1])
        if dist == -1:
            return -1
        total += dist
    return total

def nonloop_path(previous_path = [START], end = END):
    current_node  = previous_path[-1]
    new_path_list = []
    for next_node in EDGE[current_node]:
        new_path = previous_path[:]        
        if next_node not in new_path:
            new_path.append(next_node)
            new_path_list.append(new_path)
            next_new_path_list = nonloop_path(new_path, end)
            for next_new_path in next_new_path_list:
                new_path_list.append(next_new_path)            
    return new_path_list

def valid_nonloop_path(previous_path = [START], end = END):
    return [x for x in nonloop_path(previous_path, end) if x[-1] == END]

print valid_nonloop_path()