Multilevel Network Reification: Representing Higher Order Adaptivity in a Network

In this paper it is shown how a network can be extended by adding explicit states representing the characteristics defining the structure of the network. Adding such states provides what is called network reification, which can be used to explitly represent network adaptation principles. But also the adaptivity principles may change, based on second-order adaptivity of the network. By another reification step applied to the reified network, also the characteristics of such second-order adaptivity are explicitly represented, thus obtaining multilevel network reification. The construction of multilevel reification introduced here enables representation within a network not only of first-order adaptation principles, but also of second-order adaptation principles expressing change of first-order adaptation principles. The approach is illustrated for an adaptive Social Network involving an adaptive adaptation principle from Social Science based on homophily, by which connections are changing by a first-order adaptation principle which changes over time by a second-order adaptation principle.