  This paper studies the general multi-antenna multiple-relay network. Every
two nodes of the network are either connected together through a Rayleigh
fading channel or disconnected. We study the ergodic capacity of the network in
the high SNR regime. We prove that the traditional amplify-forward relaying
achieves the maximum multiplexing gain of the network. Furthermore, we show
that the maximum multiplexing gain of the network is equal to the minimum
vertex cut-set of the underlying graph of the network, which can be computed in
polynomial time in terms of the number of network nodes. Finally, the argument
is extended to the multicast and multi-access scenarios.
