Kruskal_test.txt

Python 2.7.8 (default, Jun 30 2014, 16:08:48) [MSC v.1500 64 bit (AMD64)] on win32
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>>> ================================ RESTART ================================
>>> 
enter the number of nodes in the graph
10
enter the Node no:1's key
a
enter the Node no:2's key
b
enter the Node no:3's key
c
enter the Node no:4's key
d
enter the Node no:5's key
e
enter the Node no:6's key
f
enter the Node no:7's key
g
enter the Node no:8's key
h
enter the Node no:9's key
i
enter the Node no:10's key
j
enter the number of edges in the graph
21
For the Edge no:1
of the 2 nodes involved in this edge 
enter the first Node's key
a

enter the second Node's key
b

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:2
of the 2 nodes involved in this edge 
enter the first Node's key
a

enter the second Node's key
c

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:3
of the 2 nodes involved in this edge 
enter the first Node's key
a

enter the second Node's key
f

enter the cost (or weight) of this edge (or arc) - an integer
8
For the Edge no:4
of the 2 nodes involved in this edge 
enter the first Node's key
a

enter the second Node's key
j

enter the cost (or weight) of this edge (or arc) - an integer
18
For the Edge no:5
of the 2 nodes involved in this edge 
enter the first Node's key
b

enter the second Node's key
c

enter the cost (or weight) of this edge (or arc) - an integer
3
For the Edge no:6
of the 2 nodes involved in this edge 
enter the first Node's key
b

enter the second Node's key
e

enter the cost (or weight) of this edge (or arc) - an integer
6
For the Edge no:7
of the 2 nodes involved in this edge 
enter the first Node's key
c

enter the second Node's key
e

enter the cost (or weight) of this edge (or arc) - an integer
4
For the Edge no:8
of the 2 nodes involved in this edge 
enter the first Node's key
c

enter the second Node's key
d

enter the cost (or weight) of this edge (or arc) - an integer
2
For the Edge no:9
of the 2 nodes involved in this edge 
enter the first Node's key
c

enter the second Node's key
f

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:10
of the 2 nodes involved in this edge 
enter the first Node's key
d

enter the second Node's key
e

enter the cost (or weight) of this edge (or arc) - an integer
2
For the Edge no:11
of the 2 nodes involved in this edge 
enter the first Node's key
d

enter the second Node's key
f

enter the cost (or weight) of this edge (or arc) - an integer
8
For the Edge no:12
of the 2 nodes involved in this edge 
enter the first Node's key
d

enter the second Node's key
g

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:13
of the 2 nodes involved in this edge 
enter the first Node's key
e

enter the second Node's key
g

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:14
of the 2 nodes involved in this edge 
enter the first Node's key
f

enter the second Node's key
g

enter the cost (or weight) of this edge (or arc) - an integer
7
For the Edge no:15
of the 2 nodes involved in this edge 
enter the first Node's key
f

enter the second Node's key
i

enter the cost (or weight) of this edge (or arc) - an integer
9
For the Edge no:16
of the 2 nodes involved in this edge 
enter the first Node's key
f

enter the second Node's key
j

enter the cost (or weight) of this edge (or arc) - an integer
10
For the Edge no:17
of the 2 nodes involved in this edge 
enter the first Node's key
g

enter the second Node's key
i

enter the cost (or weight) of this edge (or arc) - an integer
5
For the Edge no:18
of the 2 nodes involved in this edge 
enter the first Node's key
g

enter the second Node's key
h

enter the cost (or weight) of this edge (or arc) - an integer
4
For the Edge no:19
of the 2 nodes involved in this edge 
enter the first Node's key
h

enter the second Node's key
i

enter the cost (or weight) of this edge (or arc) - an integer
1
For the Edge no:20
of the 2 nodes involved in this edge 
enter the first Node's key
h

enter the second Node's key
j

enter the cost (or weight) of this edge (or arc) - an integer
4
For the Edge no:21
of the 2 nodes involved in this edge 
enter the first Node's key
i

enter the second Node's key
j

enter the cost (or weight) of this edge (or arc) - an integer
3
enter the maximum weight possible for any of edges in the graph
20

The edges with thier unsorted weights are
{('g', 'e'): [9], ('b', 'c'): [3], ('e', 'd'): [2], ('h', 'i'): [1], ('d', 'e'): [2], ('i', 'h'): [1], ('f', 'd'): [8], ('c', 'b'): [3], ('e', 'c'): [4], ('a', 'b'): [9], ('g', 'd'): [9], ('c', 'f'): [9], ('f', 'a'): [8], ('e', 'g'): [9], ('d', 'f'): [8], ('d', 'g'): [9], ('c', 'a'): [9], ('h', 'j'): [4], ('e', 'b'): [6], ('i', 'g'): [5], ('d', 'c'): [2], ('c', 'e'): [4], ('g', 'h'): [4], ('b', 'a'): [9], ('i', 'j'): [3], ('j', 'h'): [4], ('a', 'f'): [8], ('j', 'a'): [18], ('i', 'f'): [9], ('f', 'j'): [10], ('c', 'd'): [2], ('h', 'g'): [4], ('f', 'c'): [9], ('g', 'i'): [5], ('j', 'f'): [10], ('g', 'f'): [7], ('j', 'i'): [3], ('b', 'e'): [6], ('f', 'g'): [7], ('a', 'c'): [9], ('a', 'j'): [18], ('f', 'i'): [9]}

After sorting
[(('h', 'i'), [1]), (('i', 'h'), [1]), (('e', 'd'), [2]), (('d', 'e'), [2]), (('d', 'c'), [2]), (('c', 'd'), [2]), (('b', 'c'), [3]), (('c', 'b'), [3]), (('i', 'j'), [3]), (('j', 'i'), [3]), (('e', 'c'), [4]), (('h', 'j'), [4]), (('c', 'e'), [4]), (('g', 'h'), [4]), (('j', 'h'), [4]), (('h', 'g'), [4]), (('i', 'g'), [5]), (('g', 'i'), [5]), (('e', 'b'), [6]), (('b', 'e'), [6]), (('g', 'f'), [7]), (('f', 'g'), [7]), (('f', 'd'), [8]), (('f', 'a'), [8]), (('d', 'f'), [8]), (('a', 'f'), [8]), (('g', 'e'), [9]), (('a', 'b'), [9]), (('g', 'd'), [9]), (('c', 'f'), [9]), (('e', 'g'), [9]), (('d', 'g'), [9]), (('c', 'a'), [9]), (('b', 'a'), [9]), (('i', 'f'), [9]), (('f', 'c'), [9]), (('a', 'c'), [9]), (('f', 'i'), [9]), (('f', 'j'), [10]), (('j', 'f'), [10]), (('j', 'a'), [18]), (('a', 'j'), [18])]
 

In the graph with these vertex's
['a', 'c', 'b', 'e', 'd', 'g', 'f', 'i', 'h', 'j']

 With these edges between the vertexes given above, we obtain a Minimal Spanning Tree

{('b', 'c'): [3], ('g', 'f'): [7], ('e', 'd'): [2], ('h', 'i'): [1], ('g', 'h'): [4], ('f', 'd'): [8], ('f', 'a'): [8], ('d', 'c'): [2], ('i', 'j'): [3]}

 Please note this is a dictionary with  key as the weight of the edge and value as the key's of the two vertex's involved in this edge
>>>