In this talk, we consider the multi-agent average-consensus problem in the presence of network interference. While communicating locally with its neighbors, each agent causes additive interference in other communication links. We cast an algebraic structure over the interference and study the network interference in a variety of practical situations. We show that consensus (or distributed averaging) is possible in a low-dimensional subspace of the initial conditions, whose dimension is complimentary to the largest interference subspace across all of the agents. In this context, we derive a global information alignment and a local pre-conditioning, followed by local consensus iterations to ensure subspace consensus.