Mapping dynamical states to structural classes for Boolean networks using a classification algorithm

Complex systems have received growing interest recently, due to their universal presence in all areas of science and engineering. Complex networks represent a simplified description of the interactions present in such systems. Boolean networks were introduced as models of gene regulatory networks. Simple enough to be computationally tractable, they capture the rich dynamical behaviour of complex networks. Structure-dynamics relationships in Boolean networks have been investigated by inferring a particular structure of a network from the time sequence of its dynamical states. However, general properties of network structures, which can be obtained from their dynamics, are lacking. We create a mapping of dynamical states to structural classes, using time-delayed normalized mutual information, in an ensemble approach. The high accuracy of our classification algorithm proves that structural information is embedded in network dynamics and that we can extract it with information-theoretic methods.