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class Line(object):
    def __init__(self, fid, points):
        self.fid = fid
        self.points = points
    
    def __eq__(self, other):
        return all(any(s == o for o in other.points) for s in self.points)

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return any(self.points[0] == o for o in other.points) and any(self.points[1] == o for o in other.points)

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return (self.points[0] == other.points[0] or self.points[0] == other.points[1]) 
            and (self.points[1] == other.points[0] or self.points[1] == other.points[1])

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def create_points(data):
    points = {}
    for point_data in data:
        fid = point_data[1][0][0]
        points[fid] = Point(fid, point_data[1][0][1])
        
        fid = point_data[1][1][0]
        points[fid] = Point(fid, point_data[1][1][1])
    return points

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class Line(object):
    def __init__(self, fid, points):
        self.fid = fid
        self.points = tuple(points)
    
    def __cmp__(self, other):
        return cmp(sorted(self.points), sorted(other.points))
    
    def __hash__(self):
        return hash(tuple(sorted(self.points)))

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>>> from shapely.geometry import Polygon
>>> p1 = Polygon([(0,0),(0,2),(1,1)])
>>> print p1.area
1.0
>>> p2 = Polygon([(0,0),(0,2),(-1,-1)])
>>> print p2.area
1.0
>>> p1.touches(p2)
True
>>>

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>>> p3 = Polygon([(0,2),(0,4),(3,1)])
>>> p2.touches(p3)
True
>>> p1.touches(p3)
True

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>>> i = p1.intersection(p2)
>>> print i
LINESTRING (0.0000000000000000 0.0000000000000000, 0.0000000000000000 2.0000000000000000)
>>> j = p2.intersection(p3)
>>> print j
POINT (0.0000000000000000 2.0000000000000000)

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>>> p1.relate(p2)
'FF2F11212'

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from shapely.geometry import Point

class Node(object):
    
    def __init__(self, id, geom):
        self.id = id
        self.geom = geom
        
p1 = Node(1, Point(1,1,1))
p2 = Node(2, Point(2,2,2))
p3 = Node(3, Point(1,1,1))
p4 = Node(4, Point(4,4,4))

for pa in (p1,p2,p3,p4):
    for pb in (p1,p2,p3,p4):
        print pa.id, pb.id, pa.geom.equals(pb.geom)

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1 1 True
1 2 False
1 3 True
1 4 False
2 1 False
2 2 True
2 3 False
2 4 False
3 1 True
3 2 False
3 3 True
3 4 False
4 1 False
4 2 False
4 3 False
4 4 True