Finding and representing connectivity in pairs

I have an Nx2 matrix with numbers that tells me about pairing. What I want to do is find a way to represent the pairs and find connected graphs using it. An example input would be:

     1     2
     3     4
     3     5
     6     7
     4     7
     4     5
     4     8
     4     9
     7     5
     7     8
     7    10
     7     9
     7    11
     7    12
     5    13
     5     8
     5    11
     5    12
    14    15
    14    16
    17    18
     8    10
     8     9
     8    11
    10    11
    10    12
     9     2
    11    12

How could I use this to represent a connected graph? I would then like to get the subgraphs and be able to compare them to others so I could see if they repeat. This has been causing me issues because I'm not even sure where to start. Thank you in advance!

EDIT: I was able to find this : https://www.mathworks.com/matlabcentral/newsreader/view_thread/168883

I could make it so that I create a matrix of 1's and 0's, would that work?

Answer 1

[Image Analyst]

Why not just use unique() to check for repeats and ismember() to check if the pairs exist in another data set?

[Sam]

Maybe my whole problem has been overcomplicated this, but wouldn't that not give me the subgraphs with the structure? So if I see that 8 - 1, 3 - 8, 10 - 1, how would doing unique and ismember help me in finding that? I understand after getting the results I would just run through and check if it's a member.

[Image Analyst]

It wouldn't give you a graph but I didn't see why that was needed after hearing what you want to do: just find repeats and pairs common with another set.

[Sam]

I'm really sorry but I'm not thinking very well right now. Could you by any chance walk me through your idea using the input I gave as an example? It would really help in my understanding.

[Sam]

Perhaps I could just make a matrix and use this function? https://www.mathworks.com/matlabcentral/newsreader/view_thread/168883