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The topology of interactions is shaping dynamics of complex systems. Here, the authors develop a quantitative method to determine how much higher-order structure can be reduced without affecting dynamical behavior, revealing when higher-order interactions matter.

Many real-world systems involve higher-order, directional interactions that are naturally modeled by directed hypergraphs. The authors develop a framework that characterizes directed hypergraphs through hyperedge pattern frequencies, frequent co-sending and co-receiving nodes, higher-order reciprocity, and motifs, revealing their microscale organization.

Battiston et al. discuss the emerging paradigm of higher-order network science and its applications to social systems and human dynamics.

Group interactions can lead to explosive onsets of collective behaviors in biological and sociotechnological systems. Here, the authors show that it is the overlap between these kind of higher-order interactions that drives whether emergence of synchrony and epidemics shows up smoothly or abruptly.

Gamma-ray bursts (GRBs) are known to have impact on Earth’s lower ionosphere, but GRB impacts on the upper ionosphere was not observed before. Here, the authors show strong electric field variation at 500 km in the ionosphere caused by GRB221009A.

Understanding how team dynamics impact performance in collaborative environments remains an open question. Here, authors use fine-grained activity data from software projects to characterize team evolution, showing how team-level changes unfold and how leadership change links to greater success.

Here, the authors perform a higher-order analysis of fMRI data, revealing that accounting for group interactions greatly enhances task decoding, brain fingerprinting, and brain-behavior associations compared to traditional methods, offering a new insight into brain dynamics.

Network memory impacts dynamical processes emerging in real-world social systems, however little is known about memory of temporal networks beyond pairwise interactions. The authors develop a framework to characterize the temporal organization of higher-order networks and propose a model of temporal hypergraphs with higher-order memory to reproduce the patterns emerging in real-world complex systems.

An analysis of the number of physicists and their career paths reveals the changing landscape of the physics subdisciplines, highlighting the connections between different fields and the effects of large collaborations.

Networks with higher-order interactions are known to provide better representation of real networked systems. Here the authors introduce a framework based on statistical inference to detect overlapping communities and predict hyperedges of any size in hypergraphs.

Complex real-world networks with higher-order interactions can be described and analyzed using two types of representation, simplicial complexes and hypergraphs. The authors show that choice of representation is essential and demonstrate its impact on emerging collective dynamics in the network.

Most temporal analyses of multivariate time series rely on pairwise statistics. A study combining network theory and topological data analysis now shows how to characterize the dynamics of signals at all orders of interactions in real-world data.

Alvarez-Rodriguez et al. examine group interactions by means of higher-order social networks. They propose a theoretical framework for studying real-world interactions and provide a case study of collaboration in science and technology.

Annually, the European Research Council (ERC) and the National Science Foundation (NSF) allocate resources to promote research excellence in Europe and the USA. We observe that European Union (EU)-based researchers rely strongly on United States (US) collaborations to secure top EU funding, while the reverse is much less common.

Graph similarity measures are essential for downstream tasks including clustering, embedding, and regression with populations of networks. Here the authors derive a family of graph mutual information measures that allow for a principled, interpretable, and efficient comparison of networks at multiple scales.

Success is being increasingly studied as a collective phenomenon. Here the authors review how this perspective has deepened our understanding of success, uncovering regularities and predictive signals across diverse domains, as well as biases that challenge meritocratic views of success.

The increasing availability of new data on biological and sociotechnical systems highlights the importance of well grounded filtering techniques to separate meaningful interactions from noise. In this work the authors propose the first method to detect informative connections of any order in statistically validated hypergraphs, showing on synthetic benchmarks and real-world systems that the highlighted hyperlinks are more informative than those extracted with traditional pairwise approaches.

Recent research has shown that pair interactions in a given network are superseded by higher-order interactions and to incorporate these features into our understanding of a network additional mathematical tools, such as hypergraphs, are required. Here, the authors develop an algorithm to detect motifs in hypergraphs and show how they can be used to identify structural differences in a variety of real-world systems.

Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.

A protocol for quantitative MRI of the spinal cord using 3T MRI systems from the three main manufacturers: GE, Philips and Siemens. The authors offer guidance for assessing macrostructural and microstructural integrity using various imaging approaches.

What is the path towards a physical theory of complex networked systems? With an eye to the historical maths-physics duality, and an outlook towards the future, this commentary discusses promises and challenges accompanying the convergence of formal graph theory and data-inspired network science.