  The interconnection network comprises a significant portion of the cost of
large parallel computers, both in economic terms and power consumption. Several
previous proposals exploit large-radix routers to build scalable low-distance
topologies with the aim of minimizing these costs. However, they fail to
consider potential unbalance in the network utilization, which in some cases
results in suboptimal designs. Based on an appropriate cost model, this paper
advocates the use of networks based on incidence graphs of projective planes,
broadly denoted as Projective Networks. Projective Networks rely on highly
symmetric generalized Moore graphs and encompass several proposed direct (PN
and demi-PN) and indirect (OFT) topologies under a common mathematical
framework. Compared to other proposals with average distance between 2 and 3
hops, these networks provide very high scalability while preserving a balanced
network utilization, resulting in low network costs. Overall, Projective
Networks constitute a competitive alternative for exascale-level
interconnection network design.
