Since the beginning of the research on the dynamics of complex networks, the deep relationship between topology and dynamics has been thoroughly explored with regard the synchronization between the nodes’ dynamics, and the knowledge gathered so far has driven the advance in crucial applications.
However, there are cases in which the system performs its activity in a partial or weakly synchronization regime to preserve the balance between functional integration and segregation, whereas full synchronization is pathological. But even in this far from synchronized state, each coupled unit is encoding in its own dynamics the signature of its structural role. We explore how this prominent feature could be used to extract information about the network, without having the need to make any reference to pairwise correlations, even in those situations where the structure is unknown. The effect of the coupling strength against the dynamical complexity of the nodes is found to be a function of their topological roles, with nodes of higher degree displaying lower levels of complexity (Fig. 1). 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 [1].
Figure 1: Averaged k-class complexity Ck as a function of coupling in scale-free networks.
References (optional)
[1] A. Tlaie, I. Leyva, R. Sevilla-Escoboza,V. P. Vera-Avila and I. Sendiña-Nadal. Phys. Rev. E 99, 012310 (2019).