The architecture of complex systems

In the last few years the research on networks has taken different directions producing rather unexpected and important results. Researchers have: 1) proposed various global variables to describe and characterize the properties of real-world networks; 2) developed different models to simulate the formation and the growth of networks as the ones found in the real world. The results obtained can be summed up by saying that statistical physics has been able to capture the structure of many diverse systems within a few common frameworks, though these common frameworks are very dierent from the regular array, or the random connectivity, previously used to model the network of a complex system. Here we present a list of some of the global quantities introduced to characterize a network: the characteristic path length L, the clustering coefficient C, the global efficiency Eglob, the local efficiency Eloc, the cost Cost, and the degree distribution P(k).We also review two classes of networks proposed: smallworld and scale-free networks. We conclude with a possible application of the nonextensive thermodynamics formalism to describe scale-free networks.