  We consider the multiple unicast problem under network coding over directed
acyclic networks with unit capacity edges. There is a set of n source-terminal
(s_i - t_i) pairs that wish to communicate at unit rate over this network. The
connectivity between the s_i - t_i pairs is quantified by means of a
connectivity level vector, [k_1 k_2 ... k_n] such that there exist k_i
edge-disjoint paths between s_i and t_i. Our main aim is to characterize the
feasibility of achieving this for different values of n and [k_1 ... k_n]. For
3 unicast connections (n = 3), we characterize several achievable and
unachievable values of the connectivity 3-tuple. In addition, in this work, we
have found certain network topologies, and capacity characterizations that are
useful in understanding the case of general n.
