There are several different classes of dynamical network models. In this chapter, we will discuss the following three, in this particular order:
- Models for “dynamics on networks” These models are the most natural extension of traditional dynamical systems models. They consider how the states of components, or nodes, change over time through their interactions with other nodes that are connected to them. The connections are represented by links of a network, where the network topology is ﬁxed throughout time. Cellular automata, Boolean networks, and artiﬁcial neural networks (without learning) all belong to this class.
- Models for “dynamics of networks” These are the models that consider dynamical changes of network topology itself over time, for various purposes: to understand mechanisms that bring particular network topologies, to evaluate robustness and vulnerability of networks, to design procedures for improving certain properties of networks, etc. The dynamics of networks are a particularly hot topic in network science nowadays (as of 2015) because of the increasing availability of temporal network data .
- Models for “adaptive networks” I must admit that I am not 100% objective when it comes to this class of models, because I am one of the researchers who have been actively promoting it . Anyway, the adaptive network models are models that describe the co-evolution of dynamics on and of networks, where node states and network topologies dynamically change adaptively to each other. Adaptive network models try to unify different dynamical network models to provide a generalized modeling framework for complex systems, since many real-world systems show such adaptive network behaviors .