  We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance
of leader following consensus dynamics on directed and undirected graphs. We
first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm
of the leader following dynamics and show the tightness of the proposed bounds.
Then, we discuss the relation between the system $\mathcal{H}_{\infty}$ norm
for directed and undirected networks for specific classes of graphs, i.e.,
balanced digraphs and directed trees. Moreover, we investigate the effects of
adding directed edges to a directed tree on the resulting system
$\mathcal{H}_{\infty}$ norm. In the end, we apply these theoretical results to
a reference velocity tracking problem in a platoon of connected vehicles and
discuss the effect of the location of the leading vehicle on the overall
$\mathcal{H}_{\infty}$ performance of the system.
