Nonextensive statistical mechanics and complex scale-free networks

Abstract

One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather than on microscopic details of interactions of its elements. This viewpoint allows to naturally treat collective phenomena which are often an integral part of complex systems, such as biological or socio-economical phenomena. Much of the attraction of network theory arises from the discovery that many networks, natural or man-made, seem to exhibit some sort of universality, meaning that most of them belong to one of three classes: {\it random}, {\it scale-free} and {\it small-world} networks. Maybe most important however for the physics community is, that due to its conceptually intuitive nature, network theory seems to be within reach of a full and coherent understanding from first principles ...