Scaling of nodal resilience and influence in complex dynamical networks

In complex dynamical networks, the resilience of the individual nodes against perturbation and their influence on the network dynamics are of great interest and have been actively investigated. We consider situations where the coupling dynamics are separable, which arise in certain classes of dynamical processes including epidemic spreading, population dynamics, and regulatory processes, and derive the algebraic scaling relations characterizing the nodal resilience and influence. Utilizing synthetic and empirical networks of different topologies, we numerically verify the scaling associated with the dynamical processes. Our results provide insights into the interplay between network topology and dynamics for the class of processes with separable coupling functions.