Editorial The Structure and Dynamics of Complex Networks S. Boccaletti1and V. Latora2 December 4, 2006 1 CNR- Istituto dei Sistemi Complessi, Via Madonna del Piano, 10, 50019 Sesto Fiorentino (FI), Italy 2 Dipartimento di Fisica e Astronomia, Universit a di Catania, and INFN Sezione di Catania, Via S. Sofi a, 64, 95123 Catania, Italy Abstract This is the preface article of the Topic Issue on “Complex Networks Structure and Dynamics”, edited by Stefano Boc- caletti and Vito Latora, that will be published in July 2007, Volume 17, Issue 7, of the International Journal of Bifurcation and Chaos. http:/www.worldscinet.com/ijbc/ijbc.shtml 1 Complex networks describe a wide range of systems in fi elds as dis- parate as sociology, biology and technology. Examples include networks of acquaintances or collaborations between individuals, neural networks in the brain, or computers in telecommunication networks. The past ten years have witnessed an increasingly large attention in the physics community for the study of complex networks. This interest has certainly been triggered by the optimized rating of computing facilities, and by the grown availability of data on large real world networks (such as the Internet and the World Wide Web, electric power grids, phone call networks, the actors collaboration network in movie databases, scientifi c coauthorship and citation networks from the Science Citation Index, but also systems of interest in biology and medicine, as cortical networks or metabolic and protein networks). The massive and comparative analysis of networks from diff erent fi elds has produced a dramatic advance in the understanding of complex systems. The fi rst issue that has been faced is about the structure of complex networks. In particular, we have learned that, despite the inherent dif- ferences, most of the real world networks are characterized by similar topological properties, as for instance relatively small characteristic path lengths, high clustering coeffi cients, fat tailed shapes in the degree distri- butions, degree correlations, and the presence of motifs and community structures. Attempts to explain such similarities have led to a large at- tention to understand the evolutionary mechanisms that have shaped the topology of a network, and to the design of new models retaining the most signifi cant properties observed empirically. This fi rst stage of the research was motivated by the expectancy that the characterization and the mod- elling of the structure of a network would lead to a better knowledge of its dynamical and functional behavior. And, indeed, the second issue that has been faced concerns the study of dynamical processes on complex networks. In this context, we have learned that the coupling architecture has important consequences on the network functional robustness and response to external perturbations, as random failures, or targeted attacks.At the same time, a series of evidences 2 pointed out the crucial role played by the network topology in determining the emergence of collective dynamical behavior, such as synchronization, or in governing the main features of relevant processes that take place in complex networks, such as the spreading of epidemics, information and rumors. An increasingly larger number of works has been published after the two seminal papers, that by Watts and Strogatz on small-world net- works, appeared in Nature in 1998 Watts while the book by Pastor-Satorras and Vespignani focuses on the analysis and modelling of the Internet Pastor-Satorras covers what we believe are, today, the most important and modern aspects in the study of complex networks, and possibly also the best candidates to attract further attention in the next future. The works are divided into tutorials, papers and letters, and are orga- nized by following the natural order: fi rst works on measures, methods and models to study the structure of a network, and then works studying diff erent kinds of dynamical processes over a network. The issue opens with three tutorials. The fi rst two tutorials deal with structural issues. The fi rst, by Christensen and Albert, describes how net- work measures and models have contributed to the understanding of the organization of complex systems. The second one, by Braunstein, Wu, Chen, Buldyrev, Kalisky, Sreenivasan, Cohen, L opez, Havlin and Stanley, is about weighted networks. The authors deal with random networks with weighted links or nodes and review results on optimal paths (i.e. paths with minimum sum of the weights) and minimal spanning trees. The third tutorial, by Stoop and Wagner, is on the dynamics of neural systems. In particular, the authors show how the neocortical neurons are arranged and coupled into a network that optimizes information propa- gation and synchronizability at a minimal total connection length. The issue follows with thirteen papers. The fi rst paper, by Park, Celma, Koppenberger, Cano and Buld u, analyzes the st