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A K-core of a complex network is a cluster of nodes that are connected to at least K other nodes of the cluster. Zhao et al. show that the influence of nodes outside a percolating K-core of protected nodes determines the size of the core and may cause an abrupt breakdown of the core.

The control of a complex network can be achieved by different combinations of relatively few driver nodes. Tao Jia and colleagues show that this can lead to two distinct control modes—centralized or distributed—that determine the number of nodes that can act as driver node.

Here, using whole-metagenome shotgun sequencing data from patients with COVID-19 and controls, the authors reconstruct 11,584 microbial metagenome-assembled genomes (MAGs) including 5,403 non-redundant MAGs, revealing microbiota and metabolic pathways associations with SARS-CoV-2 infection at strain-level resolution.

Here, leveraging species-specific Type IIB restriction endonuclease digestion sites as reference instead of universal markers or whole microbial genomes, the authors introduce MAP2B, a metagenomic profiler, showing it can significantly remove false-positive identification and generate highly accurate taxonomic profiling results.

Precision nutrition requires accurate predictions of individual metabolic responses to diets. Here, authors show their deep-learning model, McMLP, outperforms existing methods in predicting metabolite responses to dietary interventions.

Here, the authors introduce METRIC, a deep-learning method that corrects measurement errors in self-reported dietary nutrient profiles using assessed data and microbial composition, effectively enhancing dietary accuracy.

Collective cooperation is found across many social and biological systems. Here, the authors find that infrequent hub updates promote the emergence of collective cooperation and develop an algorithm that optimises collective cooperation with update rates.

Understanding the decentralized self-organization in animal groups helps design swarm robotics, yet the underlying mechanism remains elusive. Xiao et al. analyze collective motions of three large bird-flocking datasets and translate their findings to guide evacuation of a swarm of miniature robots in confinement.

Using deep learning to identify the assembly rules of microbial communities from different habitats, the authors develop a framework to quantify and predict the community-specific keystoneness of each species in any microbiome sample.

Predicting the colonization of exogenous species in complex communities is a challenge in ecology. Here, the authors propose a data-driven approach to predict colonization outcomes and perform validation experiments in human gut microbial communities.

Finding the ground states of spin glasses relevant for disordered magnets and many other physical systems is computationally challenging. The authors propose here a deep reinforcement learning framework for calculating the ground states, which can be trained on small-scale spin glass instances and then applied to arbitrarily large ones.

Here, Li et al. show that functional redundancy, which has not previously been quantified at the proteome level, can arise when different microbes play similar roles in the gut microbiome, revealing that proteomes are nested among gut microbes, favoring high functional redundancy.

Ke et al. investigated the association between trauma exposure and post-traumatic stress disorder symptoms and the gut microbiome and dietary pattern of a cohort of women enrolled in a longitudinal study in the United States.

A computational method for rapid and accurate gap-filling of metabolic networks without using phenotypic data is unavailable. Here, the authors address this problem by developing a deep learning based method that can predict missing reactions using topological features of the metabolic networks.

A study shows that controlling link dynamics on a network is distinctly different from controlling the dynamics of its nodes. This development illustrates how ideas from control-systems engineering can help us better understand the organization of complex systems.

Computational models can help predict metabolic profiles of microbial communities such as human gut microbiomes or environmental microbiomes, but they lack generalizability and interpretability. To address this challenge, Wang et al. report a deep learning approach for metabolic profile prediction called mNODE that incorporates a neural network module with hidden layers described by ordinary differential equations.

Small distinctive patterns or ‘motifs’ are more prevalent in real systems than they are in randomly generated networks. It now seems that these motifs emerge naturally according to a principle that favours interconnections biased towards stability.

Here, the authors develop a genome evolution model to investigate the origin of functional redundancy in the human microbiome by analyzing its genomic content network and illustrate potential ecological and evolutionary processes that may contribute to its resilience.

Here, the authors present a theoretical framework based on community ecology and network science to investigate the efficacy of fecal microbiota transplantation in conditions associated with a disrupted gut microbiota, using the recurrent Clostridioides difficile infection as a prototype disease.

Controlling microbial communities could help restore ecosystems and maintain healthy microbiota. Here, the authors introduce the notion of structural accessibility and develop a framework to identify minimal sets of driver species, manipulation of which could allow control of a microbial community.

Population structure enables emergence of cooperation among individuals, but the impact of the dynamic nature of real interaction networks is not understood. Here, the authors study the evolution of cooperation on temporal networks and find that temporality enhances the evolution of cooperation.

Studying human diet may help us identify measures to treat or prevent chronic diseases. Here, the authors discover the nutritional redundancy phenomenon in human diet and demonstrate its association with cardiovascular disease and type 2 diabetes.

In statistical physics, the observable macroscopic behaviour of a system is obtained from a microscopic model of its components. Here, the authors extend this approach to systems with no known microscopic dynamics, by looking at the system’s response to external perturbations.

An articulation point in a network is a node whose removal disconnects the network. Here the authors develop analytical tools to study key issues pertinent to articulation points, such as the expected number of them and the network vulnerability against their removal, in arbitrary complex networks.

Network controllability has numerous applications in natural and technological systems. Here, Gao et al.develop a theoretical approach and a greedy algorithm to study target control—the ability to efficiently control a preselected subset of nodes—in complex networks.

A fundamental problem in network science is how to find an optimal set of key players whose activation or removal significantly impacts network functionality. The authors propose a deep reinforcement learning framework that can be trained on small networks to understand the organizing principles of complex networked systems.

Comprehensive understanding of the human protein-protein interaction network, aka the human interactome, can provide important insights into the molecular mechanisms of complex biological processes and diseases. Here the authors summarize the community efforts initiated by the International Network Medicine Consortium to benchmark the ability of 26 representative network-based methods to predict protein-protein interactions.

Levy et al. report a method to measure transcriptional coordination between cells in single-cell RNA sequencing data and demonstrate that transcriptional dysregulation between cells is a general phenomenon in ageing and is associated with genetic damage.

Understanding ecological interactions in microbial communities is limited by lack of informative longitudinal abundance data necessary for reliable inference. Here, Xiao et al. develop a method to infer the interactions between microbes based on their abundances in steady-state samples.

The complex interactions inherent in real-world networks grant us precise system control via manipulation of a subset of nodes. It turns out that the extent to which we can exercise this control depends sensitively on the number of nodes perturbed.

Many computational tools for metagenomic profiling have been developed, with different algorithms and features. This analysis shows that, when comparing these tools, the distinction of different types of relative sequence abundance should be taken into consideration.

A new computational method to characterize the dynamics of human-associated microbial communities is applied to data from two large-scale metagenomic studies, and suggests that gut and mouth microbiomes of healthy individuals are subjected to universal (that is, host-independent) dynamics, whereas skin microbiomes are shaped by the host environment; the method paves the way to designing general microbiome-based therapies.

Modern society relies on many interdependent networks such as electric grids, supply chain networks and ecological networks. This Perspective describes progress and challenges in harnessing insights from statistical physics and control theory to develop better control and management strategies of such complex networks and infrastructure systems.