Labyrinths.sagews

G = Graph()
G.add_vertices([1,2,3])
plot(G)

G.add_edges([(1,2),(2,3),(1,3)])
plot(G)

def getGrid(n,m):
    G = Graph()
    for i in xrange(n):
        for j in xrange(m):
            G.add_vertex((i,j))
    for i in xrange(n):
        for j in xrange(m-1):
            G.add_edge(((i,j),(i,j+1)))
    for i in xrange(n-1):
        for j in xrange(m):
            G.add_edge(((i,j),(i+1,j)))
    return G

def plotGrid(G):
    return G.plot(pos = {v:v for v in G.vertices()})

G = getGrid(3,4)
plot(G)

plotGrid(G)

G.random_spanning_tree()

[((0, 1), (0, 2)), ((0, 2), (0, 3)), ((0, 3), (1, 3)), ((1, 3), (1, 2)), ((1, 3), (2, 3)), ((2, 3), (2, 2)), ((2, 2), (2, 1)), ((2, 1), (2, 0)), ((2, 0), (1, 0)), ((0, 1), (0, 0)), ((0, 1), (1, 1))]

G.spanning_trees_count()

2415