Relating Emerging Adaptive Network Behavior to Network Structure: A Declarative Network Analysis Perspective

In this paper, the challenge for dynamic network modeling is addressed how emerging behavior of an adaptive network can be related to characteristics of the adaptive network's structure. By applying network reification, the adaptation structure is modeled in a declarative manner as a subnetwork of a reified network extending the base network. This construction can be used to model and analyze any adaptive network in a neat and declarative manner, where the adaptation principles are described by declarative mathematical relations and functions in reified temporal-causal network format. In different examples, it is shown how certain adaptation principles known from the literature can be formulated easily in such a declarative reified temporal-causal network format. The main focus of this paper on how emerging adaptive network behavior relates to network structure is addressed, among others, by means of a number of theorems of the format "properties of reified network structure characteristics imply emerging adaptive behavior properties". In such theorems, classes of networks are considered that satisfy certain network structure properties concerning connectivity and aggregation characteristics. Results include, for example, that under some conditions on the network structure characteristics, all states eventually get the same value. Similar analysis methods are applied to reification states, in particular for adaptation principles for Hebbian learning and for bonding by homophily, respectively. Here results include how certain properties of the aggregation characteristics of the network structure of the reified network for Hebbian learning entail behavioral properties relating to the maximal final values of the adaptive connection weights. Similarly, results are discussed on how properties of the aggregation characteristics of the reified network structure for bonding by homophily entail behavioral properties relating to clustering and community formation in a social network.