Analysis of Complex Networks

2.1 Introduction

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

It has become standard practice to describe networks by a set of macroscopic parameters. These parameters usually provide a practical understanding about the statistics of linking within the network, the degrees of clustering, or the statistics of occurrence of certain motives. With this knowledge it is in many cases sufficient to reliably characterize a particular network in terms of its structure, robustness, and performance or function. Often networks are not structures that are purposefully designed but that emerge as a consequence of microscopic ...