Modeling higher order adaptivity of a network by multilevel network reification

In network models for real-world domains, often network adaptation has to be addressed by incorporating certain network adaptation principles. In some cases, also higher order adaptation occurs: the adaptation principles themselves also change over time. To model such multilevel adaptation processes, it is useful to have some generic architecture. Such an architecture should describe and distinguish the dynamics within the network (base level), but also the dynamics of the network itself by certain adaptation principles (first-order adaptation level), and also the adaptation of these adaptation principles (second-order adaptation level), and may be still more levels of higher order adaptation. This paper introduces a multilevel network architecture for this, based on the notion network reification. Reification of a network occurs when a base network is extended by adding explicit states representing the characteristics of the structure of the base network. It will be shown how this construction can be used to explicitly represent network adaptation principles within a network. When the reified network is itself also reified, also second-order adaptation principles can be explicitly represented. The multilevel network reification construction introduced here is illustrated for an adaptive adaptation principle from social science for bonding based on homophily and one for metaplasticity in Cognitive Neuroscience.