Complex Networks represent the mathematical counterpart of the Complex Systems a new interdisciplinary discipline. The main core of activity is to describe all the situations in which we deal with many interacting parts. The collective behaviour arising is somewhat qualitatively different from what we would expect from looking at only one of these parts. A typical example are conductive materials. The wave function of the electron in a periodic potential produces a behaviour totally unexpected if one considers an electron in a single atom. Similarly, a series of computers linked together, a series of web pages and their hyperlilnks, a web of food predation in an environment or a set of acquaintances relations in a community, develop particular properties in the propagation of computer viruses, ideas, information.
Complex Networks are one of the more powerful (in my view) tools to describe, predict and possibly control all these systems.