Looking for a real Problem

Hi, I have been just familiar with METIS. I gave a simple graph to that and it partitioned for me. I have heard that some real problems give rise to a graph that we can give them to METIS.

I am looking for a problem like that so I can undrestand where this problem is originated from?
I am looking for a real value problems. In these problems we should have an Ax=b so we need both a matrix and a vector.

I've searched a lot of sites and papers but they all give me formulas and general information. I need a real problem and real equation like Ax=b.
I would be happy if you help me.