Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Well-established ranking algorithms (such as the popular Google's PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. The recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of real network traffic, prediction of future links, and identification of highly-significant nodes.Comment: 54 pages, 16 figure

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As new instances of nested organization-beyond ecological networks-are discovered, scholars are debating the coexistence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of in-block nestedness, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge.