  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.
