Title: Adaptive networks with preferred degree: from the mundane to the surprising
Abstract: Network studies have played a central role for understanding many systems in nature - e.g., physical, biological, and social. While static networks have been the focus in the bulk of network research, many networks in nature are dynamic. We considered this issue, in the context of social networks. In particular, We introduce a simple model of adaptive networks, modeling a society in which an individual cuts/adds links based on whether he or she has more/less links than some "preferred number" (kappa). For example, introverts/extroverts typically have small/large kappa's. Evolving with detailed balance violating dynamics, the steady state distribution of this dynamic network is not known in general, though it displays reasonably understandable properties. After a brief summary of systems with a single kappa and one with two groups with different kappa's, I will present the details of a system with "extreme introverts (I) and extroverts (E)" (kappa = 0 and infinity). With just two control parameters (i.e., the numbers of I's and E's), this system displays an extraordinary transition, known as the extreme Thouless effect. Beyond this theoretically interesting limit of our system, we outline some potentially important applications, such as modeling the response to a spreading epidemic by a population with adaptive behavior.