J an 2 00 3 Search and Congestion in Complex Networks

In recent years, the study of static and dynamical properties of complex networks has received a lot of attention [1–5]. Complex networks appear in such diverse disciplines as sociology, biology, chemistry, physics or computer science. In particular, great effort has been exerted to understand the behavior of technologically based communication networks such as the Internet [6], the World Wide Web [7], or e-mail networks [8–10]. However, the study of communication processes in a wider sense is also of interest in other fields, remarkably the design of organizations [11,12]. For instance, it is estimated that more than a half of the U.S. work force is dedicated to information processing, rather than to make or sell things in the narrow sense [11]. The pioneering work of Watts and Strogatz [1] opened a completely new field of research. Its main contribution was to show that many real-world networks have properties of random graphs and properties of regular low dimensional lattices. A model that could explain this observed behavior was missing and the proposed ”small-world” model of the authors turned the interest of a large number of scientist in the statistical mechanics community in the direction of this appealing subject. Nevertheless, this simplified model gives rise to a connectivity distribution function with an exponential form, whereas many real world networks show a highly skewed degree distribution, usually with a power law tail P (k) ∝ k (1)