Buggy python submission (verdict: Time Limit Exceeded):
import numpy
N, M = map(int, input().split())
mat = [[0 for i in range(N)] for i in range(N)]
a = [0 for i in range(M)]
b = [0 for i in range(M)]
for i in range(M):
    st = input().split()
    a[i] = int(st[0])-1
    b[i] = int(st[1])-1
    mat[a[i]][b[i]]+=1
    mat[b[i]][a[i]]+=1

ans = 0
for n in range(M):
    mtx = numpy.array(mat)
    mtx[a[n],b[n]] -= 1
    mtx[b[n],a[n]] -= 1
    roopex = numpy.zeros([N, N])
    for i in range(N):
        for j in range(N):
            if mtx[i, j] != 0:
                roopex[i, j] = 1
    rootnum = numpy.dot(mtx, mtx)
    for k in range(N):
        for i in range(N):
            for j in range(N):
                if rootnum[i, j] != 0:
                    roopex[i, j] = 1
        rootnum = numpy.dot(rootnum, mtx)
    flag = 0
    for i in range(N):
        for j in range(N):
            if roopex[i, j] == 0:
                flag = 1
                break
        if flag == 1:
            break
    if flag == 1:
        ans += 1

print(ans)


Fixed submission:
V, E = map(int, input().split())
a = [0 for i in range(E)]
b = [0 for i in range(E)]
m = [[0 for i in range(V)] for i in range(V)]
for i in range(E):
    a[i], b[i]=map(int, input().split())
    m[a[i]-1][b[i]-1]+=1
    m[b[i]-1][a[i]-1]+=1
S=0
for n in range(E):
    m[a[n]-1][b[n]-1]-=1
    m[b[n]-1][a[n]-1]-=1
    U=[[] for i in range(V)]
    for i in range(V):
        for j in range(V):
            if m[i][j]!=0:
                U[i].append(j)
    P=[set() for i in range(E+1)]
    P[0].add(0)
    Q=set()
    R=[False for i in range(V)]
    for i in range(1,E+1):
        for u in P[i-1]:
            for v in U[u]:
                if not(R[v]):
                    R[v]=True
                    P[i].add(v)
                    Q.add(v)
        if len(P[i])==0:
            break
    if len(Q)!=V:
        S+=1
    m[a[n]-1][b[n]-1]+=1
    m[b[n]-1][a[n]-1]+=1
print(S)

Buggy python submission (verdict: Runtime Error):
import numpy
N, M = map(int, input().split())
mat = [[0 for i in range(N)] for i in range(N)]
a = [0 for i in range(M)]
b = [0 for i in range(M)]
for i in range(M):
    st = input().split()
    a[i] = int(st[0])-1
    b[i] = int(st[1])-1
    mat[a[i]][b[i]]+=1
    mat[b[i]][a[i]]+=1

ans = 0
for n in range(M):
    mtx = numpy.array(mat)
    mtx[a[n],b[n]] -= 1
    mtx[b[n],a[n]] -= 1
    roopex = numpy.zeros([N, N])
    for i in range(N):
        for j in range(N):
            if mtx[i, j] != 0:
                roopex[i, j] = 1
    rootnum = numpy.dot(mtx, mtx)
    for k in range(N):
        for i in range(N):
            for j in range(N):
                if rootnum[i, j] != 0:
                    roopex[i, j] = 1
        rootnum = numpy.dot(rootnum, mtx)
    flag = 0
    for i in range(N):
        for j in range(N):
            if roopex[i, j] == 0:
                flag = 1
                break
        if flag == 1:
            break
    if flag == 1:
        ans += 1

print(ans)


Fixed submission:
V, E = map(int, input().split())
a = [0 for i in range(E)]
b = [0 for i in range(E)]
m = [[0 for i in range(V)] for i in range(V)]
for i in range(E):
    a[i], b[i]=map(int, input().split())
    m[a[i]-1][b[i]-1]+=1
    m[b[i]-1][a[i]-1]+=1
S=0
for n in range(E):
    m[a[n]-1][b[n]-1]-=1
    m[b[n]-1][a[n]-1]-=1
    U=[[] for i in range(V)]
    for i in range(V):
        for j in range(V):
            if m[i][j]!=0:
                U[i].append(j)
    P=[set() for i in range(E+1)]
    P[0].add(0)
    Q=set()
    R=[False for i in range(V)]
    for i in range(1,E+1):
        for u in P[i-1]:
            for v in U[u]:
                if not(R[v]):
                    R[v]=True
                    P[i].add(v)
                    Q.add(v)
        if len(P[i])==0:
            break
    if len(Q)!=V:
        S+=1
    m[a[n]-1][b[n]-1]+=1
    m[b[n]-1][a[n]-1]+=1
print(S)