Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

InhaltsangabeI Real-World Examples of Adaptive Networks.- Social Group Dynamics in Networks.- Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions.- Adaptive Biological Networks.- Adaptive Networks.- II Self-Organization of Adaptive Networks.- Self-Organized Criticality and Adaptation in Discrete Dynamical Networks.- Self-Organization and Complex Networks.- Self-Organization of Network Structure in Coupled-Map Systems.- Dynamical Optimization and Synchronization in Adaptive Complex Networks.- III Contact Processes and Epidemiology on Adaptive Networks.- Contact Processes and Moment Closure on Adaptive Networks.- Noise Induced Dynamics in Adaptive Networks with Applications to Epidemiology.- IV Social Games on Adaptive Networks.- A Dynamic Model of Social Network Formation.- Evolutionary Games in Self-Organizing Populations.- The Diplomat’s Dilemma: Maximal Power for Minimal Effort in Social Networks.- V Graph-Rewriting-Based Approaches.- Graph-Rewriting Automata as a Natural Extension of Cellular Automata.- Generative Network Automata: A Generalized Framework for Modeling Adaptive Network Dynamics Using Graph Rewritings.