Coevolution of information processing and topology in hierarchical adaptive random Boolean networks

Random Boolean Networks (RBNs) are frequently used for modeling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN) as a system consisting of distinct adaptive RBNs (ARBNs) – subnetworks – connected by a set of permanent interlinks. We investigate mean node information, mean edge information as well as mean node degree. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. The main natural feature of ARBNs, i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurations which is documented by power law distributions of network attractor lengths. The mean information processed by a single node or a single link increases with the number of interlinks added to the system. The mean length of network attractors and the mean steady-state connectivity possess minima for certain specific values of the quotient between the density of interlinks and the density of all links in networks. It means that the modular network displays extremal values of its observables when subnetworks are connected with a density a few times lower than a mean density of all links.