  We consider a directed acyclic network where there are two source-terminal
pairs and the terminals need to receive the symbols generated at the respective
sources. Each source independently generates an i.i.d. random process over the
same alphabet. Each edge in the network is error-free, delay-free, and can
carry one symbol from the alphabet per use. We give a simple necessary and
sufficient condition for being able to simultaneously satisfy the unicast
requirements of the two source-terminal pairs at rate-pair $(1,1)$ using vector
network coding. The condition is also sufficient for doing this using only
"XOR" network coding and is much simpler compared to the necessary and
sufficient conditions known from previous work. Our condition also yields a
simple characterization of the capacity region of a double-unicast network
which does not support the rate-pair $(1,1)$.
