Complex networks are becoming manifest in many fields of contemporary science, including mathematics, physics, computer science, biology, engineering, social sciences and economics. As part of a broad movement towards research in complex systems, scientists have recently found a striking degree of self-organization that emerges in networks representing seemingly diverse complex systems (Barabasi A L 2005 Nat. Phys. 1 68). The research subject of complex networks comprises the study of how networks emerge and evolve, what is their topology, how robust they are, what new phenomena emerge as a result of the interplay between the structure and dynamics and how can we take advantage of this knowledge for applications in a wide range of natural and man-made systems.

The challenge is to understand and accurately model the structure of complex networks to get more insight and a better understanding of their complex topology and functional behavior, since both are intimately linked. This makes the network approach particularly suitable to explore important aspects of complexity.

The last decade has witnessed a burst of research activity in the study of large systems made of many non-identical entities, whose interaction or interconnection patterns show complex network-like structures. The research community has benefited from the massive and comparative analysis of networks from different fields, which has produced a series of unexpected results and has shown that previous models proposed in mathematical graph theory are very far from reality (see e.g., Newman M E J 2003 SIAM Rev. 45 167, Boccaletti S et al 2006 Phys. Rep. 424 175).

Broadly speaking, research on such complex networks has found its focus in several directions. The first direction of research deals with the structure of networks and consists of identifying the unifying principles and statistical properties that are common to most real networks and how these can be captured via network generation models and algorithms. Another important body of work deals with spreading and percolation-like processes in complex networks, addressing a variety of phenomena ranging from disease spreading to information flow and resilience to random failures and attacks.

A third and promising branch of research has arisen in the last few years spurred by the new insights gained through network modeling. It has to do with the study of the behavior of large assemblies of dynamical and nonlinear systems interacting via complex topologies. Phenomena such as synchronization, the emergence of cooperation in social and biological systems, as well as signaling and gene regulatory dynamics and other biochemical processes are now being tackled with a fresh viewpoint by considering both sources of entangled complexity: the structure and the dynamics of the system's constituents. Finally, due to adaptive and dynamical wiring, networks are also dynamical entities, whose topologies evolve and adapt in time. This is another field of research which is just emerging with promising applications to a number of areas including wireless communication systems and brain dynamics.

Though modern network theory has produced a number of relevant results in the last few years, it is still at an early stage, particularly when it comes to applications in real systems and to the comprehension of the relation between their structure and function (dynamics).

The subject of complex networks is highly interdisciplinary and physicists are making important contributions to the theory, with applications to areas as diverse as computer science, mathematical epidemiology, social and biological sciences, etc. This spirit is reflected in the present issue, which has collected contributions from scientists at the very forefront of the theory and applications of complex networks.

The articles that make up this Focus Issue are only examples of the wide range of topics that are explored using the tools developed during the last few years. Although important progress has been made during the last decade, our understanding of complex networked systems, their structure and dynamics, is still far from well-established. We hope that this Focus Issue will further contribute towards better understanding of complex systems.

The articles below represent the first contributions and further additions will appear.

Focus on Complex Networked Systems: Theory and Applications Contents

Beyond centrality—classifying topological significance using backup efficiency and alternative paths
Yuval Shavitt and Yaron Singer

Scatter networks: a new approach for analysing information scatter
Lada A Adamic, K Suresh and Xiaolin Shi

New approaches to model and study social networks
P G Lind and H J Herrmann

Search in spatial scale-free networks
H P Thadakamalla, R Albert and S R T Kumara

Worm epidemics in wireless ad hoc networks
Maziar Nekovee

A measure of centrality based on network efficiency
V Latora and M Marchiori

Dynamical and spectral properties of complex networks
Juan A Almendral and Albert Díaz-Guilera

Directed network modules
Gergely Palla, Illés J Farkas, Péter Pollner, Imre Derényi and Tamás Vicsek

Topology control with IPD network creation games
Jan C Scholz and Martin O W Greiner

Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks
J Poncela, J Gómez-Gardeñes, L M Floría and Y Moreno

The interplay of universities and industry through the FP5 network
Juan A Almendral, J G Oliveira, L López, Miguel A F Sanjuán and J F F Mendes

Bounding network spectra for network design
Adilson E Motter

Accelerating networks
David M D Smith, Jukka-Pekka Onnela and Neil F Johnson

Weighted network modules
Illés Farkas, Dániel Ábel, Gergely Palla and Tamás Vicsek

Analysis of a large-scale weighted network of one-to-one human communication
Jukka-Pekka Onnela, Jari Saramäki, Jörkki Hyvönen, Gábor Szabó, M Argollo de Menezes, Kimmo Kaski, Albert-László Barabási and János Kertész

Structure–function relationship in complex brain networks expressed by hierarchical synchronization
Changsong Zhou, Lucia Zemanová, Gorka Zamora-López, Claus C Hilgetag and Jürgen Kurths

Fractality and self-similarity in scale-free networks
J S Kim, K-I Goh, B Kahng and D Kim

Size reduction of complex networks preserving modularity
A Arenas, J Duch, A Fernández and S Gómez

Fractal and transfractal recursive scale-free nets
Hernán D Rozenfeld, Shlomo Havlin and Daniel ben-Avraham

Building catastrophes: networks designed to fail by avalanche-like breakdown
M Woolf, Z Huang and R J Mondragón

Structural constraints in complex networks
S Zhou and R J Mondragón

The complex network of musical tastes
Javier M Buldú, P Cano, M Koppenberger, Juan A Almendral and S Boccaletti

Shlomo Havlin, Bar-Ilan University, Ramat-Gan, Israel
Maziar Nekovee, BT Research, Martlesham, Suffolk, UK and Centre for Computational Science, University College London, UK
Yamir Moreno, Institute BIFI, University of Zaragoza, Spain