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Percolation frameworks have been used to characterize the robustness of infrastructural networks. Here, authors introduce a percolation-based framework to study resource consumption and network effectiveness in meeting the demand.

Approaches based on neural graph embeddings have shown their effectiveness for complex networks analysis, including link prediction and node classification. The authors uncover strengths and limits of neural embeddings with respect to the task of detecting communities in networks.

The percolation transition has been regarded as model-independent, namely determined by the geometry of a system but otherwise identical for bond or site percolation models. Here, the authors show the violation of this assumption both analytically and numerically for networks with null percolation thresholds.

The dismantling problem of removing the smallest set of nodes so that a given network breaks into disconnected components is hard to solve exactly. Gu and colleagues use deep reinforcement learning and a multiplex network representation to avoid the heavy computational cost.

Our understanding of how catastrophe propagates in multi-layered networks relies on theories that apply only to infinite systems. Reducing the interconnected networks to a set of decoupled graphs provides a route to probing finite sizes.

Real-world networks are rarely isolated. A model of an interdependent network of networks shows that an abrupt phase transition occurs when interconnections between independent networks are added. This study also suggests ways to minimize the danger of abrupt structural changes to real networks.

Finding an optimal shape for transport networks, represented as multilayer structures, is a challenging problem. The authors propose analytical and computational frameworks to analyze sharp transitions from symmetric to asymmetric shapes in optimal networks, that can be applied for planning and development of improved multimodal transportation systems within a city.

Complex biological, social and engineering systems operate through intricate connectivity patterns. Understanding their robustness and resilience against disturbances is crucial for applications. This Review addresses systemic breakdown, cascading failures and potential interventions, highlighting the importance of research at the crossroad of statistical physics and machine learning.

The authors identify characteristic patterns that describe the propagation of information in online social media platforms. They show that, depending on the topic, the information flows can spread as simple or complex contagion processes, operating at a critical regime.

Boolean networks modelling various biological processes are characterized by nonlinear reversible dynamics that makes their control challenging. The authors introduce extended concepts of influence and control, typically considered in the study of spreading processes, for Boolean dynamics.

Triadic interactions are higher-order interactions relevant to many real complex systems. The authors develop a percolation theory for networks with triadic interactions and identify basic mechanisms for observing dynamical changes of the giant component such as the ones occurring in neuronal and climate networks.

The binding of multidentate ligands to the surface of lead halide perovskite nanocrystals suppresses the formation of surface defects that result in halide segregation, yielding materials with efficient and colour-stable red emission.

Network embedding is a machine learning technique for construction of low-dimensional representations of large networks. Gu et al. propose a method for the identification of an optimal embedding dimension for the encoding of network structural information inspired by natural language processing.

Multiplex networks consist of a collection of interacting layers and occur in social and technological systems. Here Osat et al. investigate optimal percolation which relates to the process of optimally dismantling multiplex networks and show that simplified versions of this problem lead to error.

Higher-order interactions reveal new aspects of the interplay between topology and dynamics in complex systems. This Perspective describes the emerging field of higher-order topological dynamics and discusses the open research questions in the area.