In an earlier work [Gutman et al., Chem. Phys. Lett. 297, 428 (1998)] the average energy (E) o f graphs with n vertices and m edges was examined, in particular its dependence on n and m . The quantity (E) was computed from a set of randomly, but not uniformly, constructed (n ,m)-graphs. We have now improved our method by constructing the (n,m)-graphs uniformly, so that every (n , m)-graph has equal probability to be generated. Differences between the old and new approaches are significant only in the case of graphs with a small number o f edges.