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Havlin and colleagues quantify the freshness of a scientific team as the absence of prior collaboration among members. Papers of fresher teams are associated with higher originality and more multidisciplinary impact, with a stronger relationship among larger teams.

Overload failures propagate through hidden functional dependencies across networked systems. Here, the authors study the spatio-temporal propagation behaviour of cascading overload failures, and find that they spread radially from their origin with an approximately constant velocity.

Networks of networks are vulnerable: a failure in one sub-network can bring the rest crashing down. Previous simulations have suggested that randomly positioned networks might offer some limited robustness under certain circumstances. Analysis now shows, however, that real-world interdependent networks, where nodes are positioned according to geographical constraints, might not be so resilient.

Techniques for understanding how a system responds to an infinitesimal perturbation are well developed — but what happens when the kick gets stronger? Insight into the topology of phase space may now provide the answer.

Phase transitions are often driven by global changes, but the cause of abrupt ones is unclear. Here, authors show that internal random cascades in interdependent superconducting networks cause abrupt transitions, revealing a metastable plateau and early warning signals of system collapse.

Sudden transitions occur in many real-world systems. Here, the authors identify a mechanism where long-term microscopic changes in interaction networks accumulate over time, leading to such abrupt transitions. They demonstrate this on three types of Ising model with additional interactions.

This study introduces a concept of persistent disruption, which marks papers that disrupt previous work but remain undisrupted later, signaling lasting impact. Milestone papers are found to be consistently associated with persistent disruption.

How does a scientist’s tendency to explore a variety of topics affect their career? Here, the authors analyze scientific publication data to understand how often scientists switch topics, how topic switching has changed over time, and how it relates to research productivity.

Many properties of physical systems are known to depend on their dimension. But for complex networks—which serve to model a wide range of physical, technological and social systems—the concept of dimension has received relatively little attention so far. This study shows how the dimension of a broad class of networks can be ascertained, and demonstrates that it determines the basic properties of the networks.

Modern networks are rarely independent, instead being coupled together with many others. Thus the failure of a small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. Here, a framework is developed for understanding the robustness of interacting networks subject to such 'cascading' failures. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure.

Spreading of information, ideas or diseases can be conveniently modelled in the context of complex networks. An analysis now reveals that the most efficient spreaders are not always necessarily the most connected agents in a network. Instead, the position of an agent relative to the hierarchical topological organization of the network might be as important as its connectivity.

Networks that fail can sometimes recover spontaneously—think of traffic jams suddenly easing or people waking from a coma. A model for such recoveries reveals spontaneous ‘phase flipping’ between high-activity and low-activity modes, in analogy with first-order phase transitions near a critical point.

Complex systems can undergo abrupt transitions leading to dramatic changes in the structural properties of the system by crossing the critical point. The authors study the origin of such critical transitions in spatially embedded networks and discover processes when external intervention on microscopic level leads to macroscopic transition of the system.

Geometric insights into the structure and function of complex networks have led to exciting developments in network science. This Review Article summarizes progress in network geometry, its theory, and applications to biological, sociotechnical and other real-world networks.

Heavy traffic jams are difficult to predict due to the complexity of traffic dynamics. The authors propose a framework to unveil identifiable early signals and predict the eventual outcome of traffic bottlenecks, which may be useful for designing effective methods preventing traffic jams.

Zhou, Pei et al. develop a more realistic information cascade model that reproduces key structures of real-world diffusion trees in distinct social platforms by combining a peer-to-peer diffusion pattern with a correction for observational bias.

Humans are a network of complex physiological systems, but quantifying these diverse systems is a challenge. This study presents a method to show that each physiological state is characterized by a specific network structure, demonstrating a connection between network topology and function.

Teleconnections between tipping elements in the Earth system are unclear. Here the authors use a climate network approach to link the Amazon Rainforest Area and the Tibetan Plateau, and show that current snow cover loss on the Tibetan Plateau is an early warning signal for an approaching tipping point.

The authors develop a theoretical method to reduce the complex dynamics of a mutualistic system to a single dynamical equation, which is then used to estimate and compare the distances to a potential tipping point across systems with scaled recovery rates.

Perturbations and disturbances can bring complex networks into undesirable states in which global functionality is suppressed. Now, a recovery scheme explains how to revive a damaged network by controlling only a small number of nodes.

Systems composed of many interacting dynamic networks exhibit complicated collective dynamics. Here, the authors study failure, damage spread and recovery in two interacting networks, constructing the phase diagram and revealing the role of triple points for optimal damage repair.

A dynamic dependency framework describes general interdependent and competitive interactions between nodes in multilayer networks and is used to study spreading phenomena.

In-vivo mechanistic methods to evaluate brain neurons spontaneous firing rate can assess the mean firing rate of a given individual, and unveil additional fundamental questions in neurology: such as the nature of 1/f fluctuations at rest state fMRI.

While the reconstruction of classic monolayer networks is a widely addressed problem, accurate reconstruction of multiplex networks is still an open challenge. Here the authors propose a statistical approach that allow to achieve optimal reconstruction of multiplex networks from partial observations and knowledge of the aggregated network.

Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks has started only recently. This article reviews a general framework for modelling the percolation properties of interacting networks and the first results drawn from its study.

Urban traffic congestion reveals consistent daily patterns, termed “jam-prints”, across cities. By analyzing real-world data with an enhanced jam tree model, the authors identify consistent patterns in traffic jam costs.

The persistence of the global climate system is essential for the sustainability of natural ecosystems. This work develops a framework, generate climate and carbon flux networks and finds that the similarity of the networks in different years is 0.57 ± 0.07, implying that the system is generally stable and that the similarity decay is very small when the year gap increases.

Statistical analyses of seismicity following earthquakes of magnitude 7.5 or higher finds a reduced occurrence of mainshocks at remote distances from the epicentre which may indicate wider energy release after very large seismic events.

A variety of complex networked systems, in biology, technology, and more, have the danger of falling into a potential stable state with abnormal activity, even if they are now at a normally functioning state. This manuscript shows how supporting the activity of a small fraction of nodes can make the system safe by eliminating the undesired state.

The move to the quantum internet demands developments in communication networks that are based on quantum entanglement. The authors discuss the phenomenon of entanglement percolation in a quantum network presenting solutions to significantly accelerate the intensive computation effort involved in the process.