  Degree of freedom (DoF) region provides an approximation of capacity region
in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling
factor. In this correspondence, we analyse the DoF region and sum DoF for
unicast layered multi-hop relay wireless networks with arbitrary number of
source/destination/relay nodes, arbitrary number of hops and arbitrary number
of antennas at each node. The result is valid for quite a few message
topologies. We reveal the limitation on capacity of multi-hop network due to
the concatenation structure and show the similarity with capacitor network.
From the analysis on bound gap and optimality condition, the ultimate capacity
of multi-hop network is shown to be strictly inferior to that of single-hop
network. Linear scaling law can be established when the number of hops is
fixed. At cost of channel state information at transmitters (CSIT) for each
component single-hop network, our achievable scheme avoids routing and
simplifies scheduling.
