Rearranging trees for robust consensus

In this paper, we use the ℋ₂ norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees, and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees according to the ℋ₂ norm. Our approach for undirected trees provides a constructive method for deriving an ordering for directed trees. Further, our approach suggests a decentralized manner in which trees can be rearranged in order to improve their robustness.