Dominant vertices in regulatory networks dynamics

Discrete-time regulatory networks are dynamical systems on directed graphs with a structure that is inspired on natural systems of interacting units. Using a notion of determination between vertices, we define sets of dominant vertices, and we prove that in the asymptotic regime, the projection of the dynamics on a dominant set allows us to determine the state of the whole system at all times. We provide an algorithm to find sets of dominant vertices, and we test its accuracy on several examples. We also explore the possibility of using the dominant set characteristics as a measure of the structural complexity of networks.