The evolution of networks like the Internet, the World-Wide-Web or citations networks has attracted large interest of the community working in complex networks. In all these networks the "preferential attachment" mechanism is taking place. Nevertheless additional elements might be also relevant to describe their evolution.
In a joint work with A.-L. Barabási we have modeled the growth of complex networks using an analogy with evolutionary models. In particular we have assigned an intrinsic fitness value to each node, where the fitness is a quantity that characterizes the intrinsic quality of the node and its ability to attract new links.
In a fitness network, a node with higher fitness acquire links at a higher rate than less fit nodes. This phenomenon, also called "fit-get-richer", describe for example how a powerful search engine like Google has been able to acquire a large share of the links in a short time. (See A.-L. Barbabási book LINKED to know more about it ). Interestingly this model shows a non-equilibrium phase transition or CONDENSATION phenomenon. This model has been considered one good stylized model for Internet structure (see R. Pastor-Satorras and A. Vespignani book EVOLUTION AND STRUCTURE OF THE INTERNET: A STATISTICAL MECHANICS APPROACH). A weighted version of the fitness model is able to reproduce non trivial weight-topology correlations and condensation of the weight of the links.