  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.
