A PSPACE-complete graph nim

We build off G. Stockman's game NIMG to create a version named NEIGHBORING NIM. By reducing from GEOGRAPHY, we show that this game is PSPACE-hard. The games created by the reduction share strong similarities with UNDIRECTED (VERTEX) GEOGRAPHY and regular NIM, though these are both solvable in polynomial-time. This application of graphs can be used as a form of game sum with any rulesets, not only NIM.