The notion of complex systems has gained considerable interest across disciplines when it comes to understand natural, biological, or social structures. Although physics has been concerned with well-mixed systems or dynamical systems on lattices for a long time, complex networks have emerged in the last decade as an essential framework for describing and investigating the organization of natural and living systems. A complex network can be regarded as any collection of units, or nodes, that are interacting as a system and that are connected by directed or undirected edges. In this respect, complex networks serve as natural models to describe the organization of a diverse range of systems. The investigation of complex networks has received a rapidly increasing amount of attention and the network perspective has invaded new research fields, with examples ranging from ecology and epidemiology to neuroscience, technological systems, financial markets, and socio-economics. The science of complex networks is characterized by a strong interaction among different disciplines and between theory and applications. It is a fast growing and promising area of interdisciplinary research, new applications are being developed at an ever-increasing rate. To strengthen this field of research the program Complex Networks as a Phenomenon across Disciplines was announced by German VolkswagenStiftung in 2007 as part of the funding initiative New Conceptual Approaches to Modeling and Simulation of Complex Systems. The initiative was focused on the theory of complex networks and its main objective was the development of new methods and mathematical models to achieve at a better quantitative understanding of complexity. The initiative addressed theoreticians from a variety of scientific disciplines and allowed them to pool their expertise and to combine complementary approaches.