We consider wireless relay networks where a source node communicates to a destination node with the help of multiple intermediate relay nodes. In wireless, if a node can send information to another node, typically it can also receive information from that node. Therefore, inherently there are many possibilities for feeding back information in wireless networks. However, transmissions are not isolated but usually subject to broadcast and interference. In this paper, we ask the following question: Can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rate in such networks? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? Our main result is to show that in any arbitrary Gaussian relay network with bidirected edges and cycles, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. The edges of this subnetwork can be identified as the information carrying links, and the remaining links as feedback, which can only provide limited contribution to capacity.