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Ubiquitous in nature and everyday life, complex networks find application in a wide variety of technological, sociological and biological systems. This work describes topological properties of networks and processes occurring in them. How do networks behave? What are the main features of a network that govern their robustness or failure?§Can the lessons of regular fractals be useful to the understanding of highly complex networks? How does dimensionality affect processes happening in them? §§After a thorough introduction giving explicit examples of a variety of real-world networks and their basic properties, this work describes several network models and their applications, including an extensive study of diffusion, the Einstein relation, and percolation in inhomogeneous complex networks.
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