  A large number of complex systems, naturally emerging in various domains, are
well described by directed networks, resulting in numerous interesting features
that are absent from their undirected counterparts. Among these properties is a
strong non-normality, inherited by a strong asymmetry that characterizes such
systems and guides their underlying hierarchy. In this work, we consider an
extensive collection of empirical networks and analyze their structural
properties using information theoretic tools. A ubiquitous feature is observed
amongst such systems as the level of non-normality increases. When the
non-normality reaches a given threshold, highly directed substructures aiming
towards terminal (sink or source) nodes, denoted here as leaders, spontaneously
emerge. Furthermore, the relative number of leader nodes describe the level of
anarchy that characterizes the networked systems. Based on the structural
analysis, we develop a null model to capture features such as the
aforementioned transition in the networks' ensemble. We also demonstrate that
the role of leader nodes at the pinnacle of the hierarchy is crucial in driving
dynamical processes in these systems. This work paves the way for a deeper
understanding of the architecture of empirical complex systems and the
processes taking place on them.
