Mathematical analysis of the emergence of communities based on coevolution of social contagion and bonding by homophily

In this paper it is analysed how community formation in an adaptive network for bonding based on similarity (homophily) 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 for bonding based on homophily. To this end, relevant properties of the network and the adaptation principle have been identified, such as a tipping point for similarity. As one of the results, it has been found how the emergence of communities 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 persons in different communities) or 1 (for persons within one community).