Moore graphs are compact graphs. As interconnection networks, they wou
ld minimize communication costs. We show that K-1, K-2 and the Peterse
n graph are the only Moore graphs that belong to epsilon(2), that is,
are optimal in average message passing density. We also show that epsi
lon(2) is closed under the Cartesian product (X) operation. On the bas
is of these findings, a new architecture is proposed.