# return the transition matrix for a graph G
def tm(G):
    A = G.am()
    n = G.order()
    T = []
    for i in xrange(n):
        d = sum(A[i])
        if d > 0:
            rowi = []
            for j in xrange(n):
                rowi.append(quotient(A[i][j],d))
        else:
            rowi = [0 for j in xrange(n)]
            rowi[i] = 1
        T.append(rowi)
    return matrix(T).transpose()

# print a real matrix with less precision
def matprint(A, precis = 5):
    n = len(A.rows())
    for i in xrange(n):
        print "[",
        for x in A[i]:
            print (str(x)+'      ')[:precis],
        print "]"


# generate random directed graph on n vertices with probability p
# of edge formation
def diGNP(n,p):
    A = []
    for i in xrange(n):
        rowi = []
        for j in xrange(n):
           if random() < p and i != j:
               rowi.append(1)
           else:
               rowi.append(0)
        A.append(rowi)
    m = matrix(A)
    return DiGraph(m)


# 2013 Big 12 Football Win-Loss Matrices
V = ["Baylor", "Iowa State", "Kansas State", "Kansas", "Oklahoma State",\
"Oklahoma", "TCU", "Texas Tech", "Texas", "West Virginia"]

# Win-Loss matrix
# (i,j) coefficient is 1 if team j beat team i
m1 = [[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [1, 0, 1, 0, 1, 1, 1, 1, 1, 0],
 [1, 0, 0, 0, 1, 1, 0, 0, 0, 0],
 [1, 1, 1, 0, 1, 1, 1, 1, 1, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 1],
 [1, 0, 0, 0, 0, 0, 0, 0, 1, 0],
 [1, 0, 1, 0, 1, 1, 0, 1, 1, 1],
 [1, 0, 1, 0, 1, 1, 0, 0, 1, 0],
 [1, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]]

# Win-Loss matrix weighted by score differentials
# (i,j) coefficient is score by which team j beat team i
m2 = [[0, 0, 0, 0, 32, 0, 0, 0, 0, 0],
 [64, 0, 34, 0, 31, 38, 4, 7, 1, 0],
 [10, 0, 0, 0, 4, 10, 0, 0, 0, 0],
 [45, 34, 21, 0, 46, 15, 10, 38, 22, 0],
 [0, 0, 0, 0, 0, 9, 0, 0, 0, 9],
 [29, 0, 0, 0, 0, 0, 0, 0, 16, 0],
 [3, 0, 2, 0, 14, 3, 0, 10, 23, 3],
 [29, 0, 23, 0, 18, 8, 0, 0, 25, 0],
 [20, 0, 0, 0, 25, 0, 0, 0, 0, 0],
 [31, 8, 23, 12, 0, 9, 0, 10, 7, 0]]