I excerpt here from the beginning of their paper.
IS THE NULL-GRAPH A POINTLESS CONCEPT?
The graph with no points and no lines is discussed critically.
Arguments for and against its official admittance as a graph
are presented. This is accompanied by an extensive survey of
the literature. Paradoxical properties of the null-graph are
noted. No conclusion is reached.
Some writers in graph theory ... have introduced to concept of a (or the)
"null-graph"--having no points and no lines; see Figure 1.
Note that it is not a question of whether the null-graph "really exists";
it is simply a question of whether there is any point in it.
ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720