Assuming some tuples represent line segments of a closed polygon, order them

order_edges.py

"""
Let's order some poly line segments!
A  B  C  D  E  F  G  H  I
0  1  2  3  4  5  6  7  8

A0     B1
  +----+
  |    |  
  |    |  
D3+    +----+F5
  |   E4    |
  |         |
  +----+----+
G6    H7   I8
"""
A, B, C, D, E, F, G, H, I, = range(9)
unord = [(E, B), (F, E), (F, I),  (H, I), (A, D), (A, B), (D, G), (H, G),]

# first sort the segments
p0, p1 = unord.pop()
ord = [(p0, p1)]
while unord:
    for pair in unord:
        if p0 in pair or p1 in pair:
            ord.append(pair)
            unord.remove(pair)
            p0, p1 = pair[0], pair[1]
            break
    else:  # break a possible infinite while
        print("malformed edge sequence")
        break
# now fix each segment's internal vertex order
unord = ord
p0, p1 = unord.pop(0)
if p1 != unord[0][0]:
    p1, p0 = p0, p1
ord = [(p0, p1)]
for pair in unord:
    if p1 == pair[0]:
        p0, p1 = pair[0], pair[1]        
    else:
        p0, p1 = pair[1], pair[0]
    ord.append((p0, p1))

print(ord)

    

# if you want the vertex points only :)
p0, p1 = ord.pop(0)
if p1 != ord[0][0]:
    p1, p0 = p0, p1
points = [p0]
for pair in ord:
    if p1 == pair[0]:
        p0, p1 = pair[0], pair[1]        
    else:
        p0, p1 = pair[1], pair[0]
    points.append(p0)