path_generator.py

def path_generator(G, a, b):
    """ Find all paths from a to b in directed graph G """
    assert all([0<=u<len(G) for u in [a,b]])
    path = []
    stack = [a]
    while stack:
        u = stack.pop()
        if u<0: # this is backtrack
            path.pop()
            continue
        else:
            stack.append(-1) # backtrack trap
            path.append(u)
            if u==b:
                yield path.copy()
                continue # not interested in any path circles back here
        stack.extend(G[u]-set(path))

G = [set([1,2]), set([3]), set([3]), set([4,5]), set([6,7]), set([6,8]), set(), set(), set()]

# Should find 4 paths
for p in path_generator(G, 0, 6):
    print(p)