Suppose that I have some data:

12,30
12,45
2,3
7,8
3,9
30, 8
45,54
56,65

Where (a,b) indicates that a is connected to b. I want to get all
connected nodes to one point. For instance, the output of the above
example should be something like:

Group 1
2,3
3,9
Group 2
12,30
12,45
30,8
7,8
Group 3
45,54
Group 4
56,65

The order is not important as long as the whole group stays together.
Reason why they are grouped like that:

1. 2 is connected to 3 and 3 is connected to 9 and so we put all the
three, i.e. 2,3,9 into one group.
2. 12 is connected to 45 and 12 is also connected to 30 so we put
these in the same group but 30 is connected to 8 and 8 is connected to
7 so ultimately we put all these into the same group.
3. 45 and 54 are connected but not related to any other numbers so we
put them into another group
4. 56 and 65 are connected but not related to any other numbers so we
put them into another group

I am unable to figure out an algorithm for this. Can someone guide me?