From robustness to resilience: A network Price identity approach

We model a closed-loop network of agents distributed among subnetworks and study the sustainability of network structures in presence of random perturbations. The model outcomes show that the stability of compartmentalized networks built on uniform operators depends on perturbations on between-subnetwork coupling, while the stability of networks built on mutation operators depends on their assimilation capacity. Through the study of eigenvalues of the Laplacian, we succeed in measuring the degree of network robustness and resilience. Our results also permit to situate the Price theorem, both in its standard and expanded forms, in the context of network evolutionary variational identity.