  We examine the $\mathcal{H}_2$ norm of matrix-weighted leader-follower
consensus on series-parallel networks. By using an extension of electrical
network theory on matrix-valued resistances, voltages and currents, we show
that the computation of the $\mathcal{H}_2$ norm can be performed efficiently
by decomposing the network into atomic elements and composition rules. Lastly,
we examine the problem of efficiently adapting the matrix-valued edge weights
to optimize the $\mathcal{H}_2$ norm of the network.
