I added this to [[Network theory]]:

The term *adaptive network* is sometimes used to denote a network whose topology changes with time in a way that interacts with dynamics on the network. For an introduction see:

* Thilo Gross and Bernd Blasius, [Adaptive coevolutionary networks: a review](http://rsif.royalsocietypublishing.org/content/5/20/259.full.html), _Journal of the Royal Society Interface_ **5** (6 March 2008), 2597–271.

A quote:

> A network consists of a number of network nodes connected by links (....) The specific pattern of connections defines the network's topology. For many applications it is not necessary to capture the topology of a given real-world network exactly in a model. Rather, in many cases the processes of interest depend only on certain topological properties (Costa et al. 2007). The majority of recent studies revolve around two key questions corresponding to two distinct lines of research: what are the values of important topological properties of a network that is evolving in time? And, how does the functioning of the network depend on these properties?

> The first line of research is concerned with the dynamics of networks. Here, the topology of the network itself is regarded as a dynamical system. It changes in time according to specific, often local, rules. Investigations in this area have revealed that certain evolution rules give rise to peculiar network topologies with special properties. Notable examples include the formation of small world (Watts & Strogatz 1998) and scale-free networks (Price 1965; Barabàsi & Albert 1999).

> The second major line of network research focuses on the dynamics on networks. Here, each node of the network represents a dynamical system. The individual systems are coupled according to the network topology. Thus, the topology of the network remains static while the states of the nodes change dynamically. Important processes that are studied within this framework include synchronization of the individual dynamical systems (Barahona & Pecora 2002) and contact processes such as opinion formation and epidemic spreading (Kuperman & Abramson 2001; Pastor-Satorras & Vespignani 2001; May & Lloyd 2001; Newman 2002; Boguñá et al. 2003). These studies have made it clear that certain topological properties have a strong impact on the dynamics. For instance, it was shown that vaccination of a fraction of the nodes cannot stop epidemics on a scale-free network (May & Lloyd 2001; Pastor-Satorras & Vespignani 2001).

> Until recently, the two lines of network research were pursued almost independently in the physical literature. While there was certainly a strong interaction and cross-fertilization, a given model would either describe the dynamics of a certain network or the dynamics on a certain network. Nevertheless, it is clear that in most real-world networks the evolution of the topology is invariably linked to the state of the network and vice versa. For instance, consider a road network. The topology of the network, that is the pattern of roads, influences the dynamic state, e.g. the flow and density of traffic. But if traffic congestions are common on a given road, it is probable that new roads will be built in order to decrease the load on the congested one. In this way a feedback loop between the state and topology of the network is formed. This feedback loop can give rise to a complicated mutual interaction between a time varying network topology and the nodes' dynamics. Networks which exhibit such a feedback loop are called coevolutionary or adaptive networks (figure 1).

The term *adaptive network* is sometimes used to denote a network whose topology changes with time in a way that interacts with dynamics on the network. For an introduction see:

* Thilo Gross and Bernd Blasius, [Adaptive coevolutionary networks: a review](http://rsif.royalsocietypublishing.org/content/5/20/259.full.html), _Journal of the Royal Society Interface_ **5** (6 March 2008), 2597–271.

A quote:

> A network consists of a number of network nodes connected by links (....) The specific pattern of connections defines the network's topology. For many applications it is not necessary to capture the topology of a given real-world network exactly in a model. Rather, in many cases the processes of interest depend only on certain topological properties (Costa et al. 2007). The majority of recent studies revolve around two key questions corresponding to two distinct lines of research: what are the values of important topological properties of a network that is evolving in time? And, how does the functioning of the network depend on these properties?

> The first line of research is concerned with the dynamics of networks. Here, the topology of the network itself is regarded as a dynamical system. It changes in time according to specific, often local, rules. Investigations in this area have revealed that certain evolution rules give rise to peculiar network topologies with special properties. Notable examples include the formation of small world (Watts & Strogatz 1998) and scale-free networks (Price 1965; Barabàsi & Albert 1999).

> The second major line of network research focuses on the dynamics on networks. Here, each node of the network represents a dynamical system. The individual systems are coupled according to the network topology. Thus, the topology of the network remains static while the states of the nodes change dynamically. Important processes that are studied within this framework include synchronization of the individual dynamical systems (Barahona & Pecora 2002) and contact processes such as opinion formation and epidemic spreading (Kuperman & Abramson 2001; Pastor-Satorras & Vespignani 2001; May & Lloyd 2001; Newman 2002; Boguñá et al. 2003). These studies have made it clear that certain topological properties have a strong impact on the dynamics. For instance, it was shown that vaccination of a fraction of the nodes cannot stop epidemics on a scale-free network (May & Lloyd 2001; Pastor-Satorras & Vespignani 2001).

> Until recently, the two lines of network research were pursued almost independently in the physical literature. While there was certainly a strong interaction and cross-fertilization, a given model would either describe the dynamics of a certain network or the dynamics on a certain network. Nevertheless, it is clear that in most real-world networks the evolution of the topology is invariably linked to the state of the network and vice versa. For instance, consider a road network. The topology of the network, that is the pattern of roads, influences the dynamic state, e.g. the flow and density of traffic. But if traffic congestions are common on a given road, it is probable that new roads will be built in order to decrease the load on the congested one. In this way a feedback loop between the state and topology of the network is formed. This feedback loop can give rise to a complicated mutual interaction between a time varying network topology and the nodes' dynamics. Networks which exhibit such a feedback loop are called coevolutionary or adaptive networks (figure 1).