Numerical measures for two-graphs

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on n vertices. Two conjectures are stated, one using these numerical measures and the other using the deck of a graph, which suggest that there is a finite set of conditions differentiating two-graphs. We verify that among the four non-trivial non-isomorphic regular two-graphs on 26 vertices that both conjectures hold.