# How do you get the highest degree from only the number of vertices and the number of edges?

I'm writing a piece of code, and in the program that I'm writing, the user of the program will enter the number of vertices and the number of edges in a graph. With the number of vertices and the number of edges, I will need to show the user the vertex with the highest degree, but the graph isn't even written. How am I supposed to find the degree of vertex just given the number of vertices and the number of edges?

You can't, except for some special cases. A small example showing that you can't is given by considering a claw graph and a $P_4$ (path graph on four vertices. Both these graphs have four vertices and three edges, but the former has maximum degree 3 and the latter maximum degree 2.