For those of us who attended Church School every week growing up, we quickly learned that if you didn’t know the answer to a a question being asked, you should just say “Jesus.” And much of the time, that was actually the right answer. As we got older that fact became more and more of a joke.
SacredSandwich.com
At BSM, a similar sort of joke has evolved, but replacing the “Jesus answer” with graph theory! A friend here told me that he has decided one of the reasons Hungarian mathematics is so strong is because they know how to simplify *any* question to one about directed graphs, connected graphs, simple graphs, bipartite graphs, etc. and then apply those theorems.
When a professor asks how we should approach the problem, and you don’t know, you should probably say “represent it as a graph.” ;)
My Math-y Adventures 
One of my favorite examples of this is how to write the permanent of a matrix as the determinant of a larger matrix. There is a proof around 30:00 of this lecture https://www.youtube.com/watch?v=6vEC99wo3AU