  We explore the relation between the topological relevance of a node in a
complex network and the individual dynamics it exhibits. When the system is
weakly coupled, the effect of the coupling strength against the dynamical
complexity of the nodes is found to be a function of their topological role,
with nodes of higher degree displaying lower levels of complexity. We provide
several examples of theoretical models of chaotic oscillators, pulse-coupled
neurons and experimental networks of nonlinear electronic circuits evidencing
such a hierarchical behavior. Importantly, our results imply that it is
possible to infer the degree distribution of a network only from individual
dynamical measurements.

Chaotic Dynamics