  Wireless fading networks with multiple antennas are typically studied
information-theoretically from two different perspectives - the outage
characterization and the ergodic capacity characterization. A key parameter in
the outage characterization of a network is the diversity, whereas a
first-order indicator for the ergodic capacity is the degrees of freedom (DOF),
which is the pre-log coefficient in the capacity expression. In this paper, we
present max-flow min-cut type theorems for computing both the diversity and the
degrees of freedom of arbitrary single-source single-sink multi-antenna
networks. We also show that an amplify-and-forward protocol is sufficient to
achieve this. The degrees of freedom characterization is obtained using a
conversion to a deterministic wireless network for which the capacity was
recently found. We show that the diversity result easily extends to
multi-source multi-sink networks and evaluate the DOF for multi-casting in
single-source multi-sink networks.
