In this work we study the communication problem in general, and show that even for the case of three sources and three terminals, a single path connecting source/terminal pairs does not suffice to communicate P Xi. We then present an efficient encoding scheme which enables the communication of P Xi for the three sources, three terminals case, given that each source terminal pair is connected by two edge disjoint paths. Our encoding scheme includes a structural decomposition of the network at hand which may be found useful for other coding problems as well.