  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, both conjectures hold.
