  Series-parallel networks are a class of graphs on which many NP-hard problems
have tractable solutions. In this paper, we examine performance measures on
leader-follower consensus on series-parallel networks. We show that a
distributed computation of the $\mathcal{H}_2$ norm can be done efficiently on
this system by exploiting a decomposition of the network into atomic elements
and composition rules. Lastly, we examine the problem of adaptively
re-weighting the network to optimize the $\mathcal{H}_2$ norm, and show that it
can be done with similar complexity.
