  Nonlinear networked systems are of interest in several areas of research,
such as multi-agent systems and social networks. In this paper, we examine the
controllability of several classes of nonlinear networked dynamics on which the
underlying graph admits negative weights. Such signed networks exhibit
bipartite clustering when the underlying graph is structurally balanced. We
show that structural balance is the key ingredient inducing uncontrollability
when combined with a leader-node symmetry and a certain type of dynamical
symmetry. We then examine the problem of extracting the bipartite structure of
such graphs from data using Extended Dynamic Mode Decomposition to approximate
the corresponding Koopman operator.
