  Criticism of Gnutella network scalability has rested on the bandwidth
attributes of the original interconnection topology: a Cayley tree. Trees, in
general, are known to have lower aggregate bandwidth than higher dimensional
topologies e.g., hypercubes, meshes and tori. Gnutella was intended to support
thousands to millions of peers. Studies of interconnection topologies in the
literature, however, have focused on hardware implementations which are limited
by cost to a few thousand nodes. Since the Gnutella network is virtual,
hyper-topologies are relatively unfettered by such constraints. We present
performance models for several plausible hyper-topologies and compare their
query throughput up to millions of peers. The virtual hypercube and the virtual
hypertorus are shown to offer near linear scalability subject to the number of
peer TCP/IP connections that can be simultaneously kept open.
