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

Abstract

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).

Context-Sensitive Control of Adaptation: Self-Modeling Networks for Human Mental Processes Using Mental Models

“…This is in strong contrast with the area of social science. Literature on adaptive social relations or adaptive social networks is available including computational models for it, such as [44,45], but although adaptation control is certainly also in this area a very relevant factor, approaches addressing the control of adaptation seems to be lacking in such literature, where only just a few more or less incidental exceptions can be found such as [6,30,34,38,39,46,47] and [31], Ch 6. Much progress would become possible for social science by explicitly addressing this issue more systematically and on a much larger scale like it was already done within neuroscience.…”

On Adaptive Networks and Network Reification

“…• From the Social Science area, in an adaptive social network based on a first-order adaptation principle for bonding based on homophily (McPherson et al 2001) the similarity measure determining how similar two persons are may change over time by a second-order adaptation principle, for example, due to age or other varying circumstances. As an example, for somebody who is very busy or already has a lot of connections the requirements for being similar might become more strict; e.g., see Treur (2018bTreur ( , 2019b and Chap. 6 in this book.…”

“…It is most often specified in the form of some procedural or algorithmic programming specification used to run the difference or differential equations underlying the network adaptation process. This non-network dynamic model interacts intensively with the dynamic model for the internal network dynamics of the base network; in Social Network context sometimes this interaction is termed co-evolution; e.g., Holme and Newman (2006), Treur (2019b). An example from the neurocognitive area is modeling Hebbian learning (Hebb 1949); this is also what is addressed in Fig.…”

Controlled Social Network Adaptation: Subjective Elements in an Objective Social World

“…This makes circular, reciprocal causal relations between the two processes. It has been found in simulations that, as in the real world, the emerging behavior of adaptive network models based on the coevolution of these two processes often shows a form of clustering, segregation or community formation (e.g., [3,4,8,14,16,17,20,21]).…”