Evolution Of Networks

Complex network theory is a modern extension of classical graph theory, driven by the recent availability of large data sets from various scientific fields that can be either directly or indirectly represented as graphs. Examples where links in the network represent explicit interactions between nodes include acquaintance networks, the world-wide web, neural networks and gene regulatory nets, to name only a few. The emergence of complex network structures and non-trivial global phenomena from local interactions is one of the main challenges in the field. For social networks, we have identified the essential dynamical ingredients necessary to obtain major non-trivial features like short path length, high clustering, and scale-free or exponential link distributions. A model based on these ingredients compares well with observational data of social networks as outlined by Davidsen et al. (2002) and Ebel et al. (2003) and has stimulated a large number of related studies on the evolution of networks.