I am an engineer working on an algorithm that solves a system of equations, where each equation is associated with an edge on a graph. Currently I am running the algorithm on a graph which has an edge between every pair of vertices (a complete graph, I believe?), but I am hoping to study the error and convergence for cases when there are fewer edges. However, when any vertex has fewer than 4 edges, the system will not converge, so I want to avoid such cases.
Is there a method to remove edges from a complete graph, such that every vertex has N edges? If not, is there anything that gets close, giving each vertex, say, N +/-M edges?
Thanks for any guidance.