Relating an Adaptive Social Network’s Structure to its Emerging Behaviour Based on Homophily

In this paper it is analysed how emerging behaviour of an adaptive network can be related to characteristics of the adaptive network’s structure, which includes the structure of the adaptation principles incorporated. In particular, this is addressed for adaptive social networks based on homophily. To this end relevant properties of the network and the adaptation principle have been identified, such as a tipping point for homophily. As one of the results it has been found how the emergence of clusters strongly depends on the value of this tipping point. Moreover, it is shown that some properties of the structure of the network and the adaptation principle entail that the connection weights all converge to 0 (for states in different clusters) or 1 (for states within a cluster)