Fregean Flows

I humbly introduce a concept I call "Fregean flows," a graph theoretic representation of classical logic, to show how higher-dimensional graph characteristics might be useful to prove or perhaps at best show the provability of simple deductive statements typically represented as one-dimensional strings of characters. I apply these to a very simple proof, namely proving the equivalence of two definitions for an Abelian group G, an if-and-only-if statement, using a re-representation of statements as vertices and both conjunctions and implications as differently coloured edges. This re-representation of an if-and-only-if is simple but shows unexpected geometry, and I discuss its possible utility in terms of provability through ideas of graph topology, similarities of graph contraction to deductive elimination, and recursion.