  We study the performance of a network of agents tasked with tracking an
external unknown signal in the presence of stochastic disturbances and under
the condition that only a limited subset of agents, known as leaders, can
measure the signal directly. We investigate the optimal leader selection
problem for a prescribed maximum number of leaders, where the optimal leader
set minimizes total system error defined as steady-state variance about the
external signal. In contrast to previously established greedy algorithms for
optimal leader selection, our results rely on an expression of total system
error in terms of properties of the underlying network graph. We demonstrate
that the performance of any given set of leaders depends on their influence as
determined by a new graph measure of centrality of a set. We define the $joint
\; centrality$ of a set of nodes in a network graph such that a leader set with
maximal joint centrality is an optimal leader set. In the case of a single
leader, we prove that the optimal leader is the node with maximal information
centrality. In the case of multiple leaders, we show that the nodes in the
optimal leader set balance high information centrality with a coverage of the
graph. For special cases of graphs, we solve explicitly for optimal leader
sets. We illustrate with examples.
