Introduction to the Modeling and Analysis of Complex Systems

Chapter 16Dynamical Networks I: Modeling16.1 Dynamical Network ModelsThere are several different classes of dynamical network models. In this chapter, we willdiscuss the following three, in this particular order:Models for “dynamics on networks” These models are the most natural extension oftraditional dynamical systems models. They consider how the states of components, ornodes, change over time through their interactions with other nodes that are connectedto them. The connections are represented by links of a network, where the networktopology is fixed throughout time. Cellular automata, Boolean networks, and artificialneural networks (without learning) all belong to this class.Models for “dynamics of networks” These are the models that consider dynamicalchanges of network topology itself over time, for various purposes: to understand mechanismsthat bring particular network topologies, to evaluate robustness and vulnerability ofnetworks, to design procedures for improving certain properties of networks, etc. The dynamicsof networks are a particularly hot topic in network science nowadays (as of 2015)because of the increasing availability of temporal network data [65].Models for “adaptive networks” I must admit that I am not 100% objective when itcomes to this class of models, because I am one of the researchers who have been activelypromoting it [66]. Anyway, the adaptive network models are models that describe theco-evolution of dynamics on and of networks, where node states and network topologies325