Understanding how biodiversity loss propagates through food web networks is essential for managing ecosystem services in agricultural landscapes. Traditional binary-topological approaches often oversimplify extinction dynamics by assuming that species go extinct only after complete resource loss. Here, we applied energetic thresholds to model secondary extinctions in 504 empirical food webs from the Farm Scale Evaluations of conventional and genetically modified herbicide-tolerant (GMHT) crop systems. We simulated species removals under varying consumer sensitivity to resource loss to assess food web robustness across crop types and management regimes. Results show that food web fragility increases with energetic thresholds, especially in GMHT-managed beet fields. Beet fields exhibit the highest levels of secondary extinction, and GMHT treatments show slightly higher extinction rates than conventional ones, suggesting increased vulnerability to species loss. Secondary extinction after single-species removals is higher in food webs lacking carnivorous links from carabids to gastropods. Keystone species shift from autotrophs to gastropods as the extinction threshold rises. Omnivory, particularly carabid-gastropod links, enhances stability by reducing secondary extinctions. These findings highlight the value of incorporating quantitative dynamics to better predict biodiversity loss and identify key species in agroecosystems, offering insights for designing more resilient agricultural systems.

Deep neural networks (DNNs) are traditionally analyzed as black-box function approximators, yet their internal structure exhibits phase transitions characteristic of complex physical systems. In this study, we investigate topological–functional decoupling—the phenomenon whereby a network retains full graph connectivity while losing computational function—in trained neural networks through the lens of percolation theory. By subjecting three distinct architectures (Shallow, Deep, and Wide MLPs) to a unified edge-pruning analysis on Fashion-MNIST, we uncover a fundamental divergence between structural integrity and computational capacity in this experimental setting. We report three key phenomena observed in these experiments: (1) the zombie network state under stochastic pruning, where the system retains global connectivity (P∞≈1.0) yet suffers a catastrophic functional collapse (accuracy falls below 50% of baseline at prunning ratio pf≈0.35–0.68 depending on depth), proves that graph reachability does not imply computational capability; (2) depth fragility, where increased network depth triggers multiplicative signal decay (the avalanche effect), rendering deep architectures exponentially more vulnerable to random edge removal than shallow ones (pfdeep≈0.35 vs. pfshallow≈0.68); and (3) scale-free universality, observed under magnitude-based pruning, where a robust functional skeleton maintains accuracy near the baseline (∼89%) up to extreme sparsity (pf≈0.85–0.95) across all three architectures. Robustness stems not from holographic redundancy in the overall connection count but from the emergent heavy-tailed rich-club organization of weight magnitudes—a sparse set of high-magnitude synapses that form the functional backbone of the network, decoupled from the redundant topological mass. These findings offer new physical constraints for the design of resilient neuromorphic hardware.

"Every object that biology studies is a system of systems." (François Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions, so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.

This study integrates network science and intersection graph theory to analyse the structural properties of recipe networks in Catalan cuisine. Using three distinct cookbooks, two traditional and one haute cuisine, we construct the recipe similarity networks by linking recipes based on shared ingredients, with link weights reflecting ingredient similarity. We introduce a new, ad hoc, similarity measure that overcomes some limitations of traditional similarity metrics. We explore how different methodological approaches, such as the substitution of recipes/ingredients with their composing ingredients and link weight normalisation, influence network structure and node centrality. Our analysis reveals that recipe similarity networks are highly interconnected but show structural differences across cuisines, particularly in haute cuisine, which features more specialised recipes. Node centrality metrics identify key recipes that define culinary traditions, such as "Allioli" in traditional Catalan cuisine and "Becada con brioche de su salmis" in haute cuisine. We also develop a community detection algorithm based on link removal and clique identification, which uncovers tightly-knit recipe groups. This study advances the field of computational gastronomy by providing a methodological foundation that can be integrated with artificial intelligence techniques to support recipe personalisation, food recommendations, and gastronomic innovation.

Weight thresholding (WT) is a method intended to decrease the number of links within weighted networks that may otherwise be excessively dense for network science applications. WT aims to remove links to simplify the network by holding most of the features of the original network. Here, we test the robustness and the efficacy of the node attack strategies on real-world networks subjected to WT that remove links of higher weight (strong links). We measure the network robustness along node removal with the largest connected component (LCC). We find that the real-world networks under study are generally robust when subjected to WT. Nonetheless, WT with strong link removal changes the efficacy of the attack strategies and the rank of node centralities. Also, WT with strong link removal may trigger a more significant change in the node centrality rank than WT by removing weak links. Network science research with the aim to find important/influential nodes in the network has to consider that simplifying the network with WT methodologies may change the node centrality.

This review underscores the critical significance of incorporating networks science in epidemiology. Classic mathematical compartmental models (CMs) employed to describe epidemic spreading may fail to capture the intricacies of real disease dynamics. Rooted in the mean-field assumption, CMs oversimplify by assuming that every individual has the potential to “infect” any other, neglecting the inherent complexity of underlying network structures. Since social interactions follow a networked pattern with specific links between individuals based on social behaviors, joining classic CMs and network science in epidemiology becomes essential for a more authentic portrayal of epidemic spreading. This review delves into noteworthy research studies that, from various perspectives, elucidate how the synergy between networks and CMs can enhance the accuracy of epidemic descriptions. In conclusion, we explore research prospects aimed at further elevating the integration of networks within the realm of epidemiology, recognizing its pivotal role in refining our understanding of disease dynamics.

Recent studies have shown correlations between the microbiota's composition and various health conditions. Machine learning (ML) techniques are essential for analyzing complex biological data, particularly in microbiome research. ML methods help analyze large datasets to uncover microbiota patterns and understand how these patterns affect human health. This study introduces a novel approach combining statistical physics with the Monte Carlo (MC) methods to characterize bacterial species in the human microbiota. We assess the significance of bacterial species in different age groups by using notions of statistical distances to evaluate species prevalence and abundance across age groups and employing MC simulations based on statistical mechanics principles. Our findings show that the microbiota composition experiences a significant transition from early childhood to adulthood. Species such as Bifidobacterium breve and Veillonella parvula decrease with age, while others like Agathobaculum butyriciproducens and Eubacterium rectale increase. Additionally, low-prevalence species may hold significant importance in characterizing age groups. Finally, we propose an overall species ranking by integrating the methods proposed here in a multicriteria classification strategy. Our research provides a comprehensive tool for microbiota analysis using statistical notions, ML techniques, and MC simulations.

Systematic experimental investigations are reported of charge transport in double-comb and star-shaped planar arrays obtained by coupling superconducting islands via Josephson tunnel junctions. The fabrication of the structures is based on a standard niobium trilayer technology with superconducting transition temperature close to 9 K. Noticeable enhancements of Josephson supercurrents and energy gap are recorded. Complementarity between experimental data and theoretical predictions is employed as a tool to clarify the role of different graph topologies in conditioning the singular behavior of synthetic graph-shaped networks. The predictions of the theoretical models are based on the Bose-Einstein topological condensation and a de Gennes-Alexander approach for granular superconductors. Evidence is shown of the dependence, for both gap and Josephson critical currents, on node-to-node connections in the networks, namely on array topology.

In this study, we simulate the degree and betweenness node attack over a large set of 200 real-world networks from different areas of science. We perform an initial node attack approach, where the node centrality rank is computed at the beginning of the simulation, and it is not updated along the node removal process. We quantify the network damage by tracing the largest connected component (LCC) and evaluate the network robustness with the “percolation threshold qc,” i.e., the fraction of nodes removed, for which the size of the LCC is quasi-zero. We correlate qc with 20 network structural indicators (NSIs) from the literature using single linear regression (SLR), multiple linear regression (MLR) models, and the Pearson correlation coefficient test. The NSIs cover most of the essential structural features proposed in network science to describe real-world networks. We find that the Estrada heterogeneity (EH) index, evaluating the degree difference of connected nodes, best predicts qc. The EH index measures the network node degree heterogeneity based on the difference of functions of node degrees for all pairs of linked nodes. We find that the qc value decreases as a function of the EH index, unveiling that heterogeneous real-world networks with a higher variance in the degree of connected nodes are more vulnerable to node attacks.

Network science offers powerful tools to model complex social systems. Most social network science research focuses on topological networks by simply considering the binary state of the links, i.e., their presence or absence. Nonetheless, complex social systems present heterogeneity in link interactions (link weight), and accounting for this heterogeneity, it is mandatory to design reliable social network models. Here, we revisit the topic of weighted social networks (WSNs). By summarizing the main notions, findings, and applications in the field of WSNs, we outline how WSN methodology may improve the modeling of several real problems in social sciences. We are convinced that WSNs may furnish ideas and insights to open interesting lines of new research in the social sciences.

In this study, we investigate the effect of weight thresholding (WT) on the robustness of real-world complex networks. Here, we assess the robustness of networks after WT against various node attack strategies. We perform WT by removing a fixed fraction of weak links. The size of the largest connected component indicates the network's robustness. We find that real-world networks subjected to WT hold a robust connectivity structure to node attack even for higher WT values. In addition, we analyze the change in the top 30% of central nodes with WT and find a positive correlation in the ranking of central nodes for weighted node centralities. Differently, binary node centralities show a lower correlation when networks are subjected to WT. This result indicates that weighted node centralities are more stable indicators of node importance in real-world networks subjected to link sparsification.

Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks and is an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node centralities for network dismantling with effective node removal strategies from the literature, namely betweenness, closeness, degree, and k-shell node removal, for synthetic and real-world networks. We evaluate the dismantling of the network by using the size of the largest connected component (LCC). We find that the degree nodes attack is the best strategy overall, and the new node removal strategies based on RW show the highest efficacy in regard to peculiar network topology. Specifically, RW strategy based on covering time emerges as the most effective strategy for a synthetic lattice network and a real-world road network. Our results may help researchers select the best node attack strategies in a specific network class and build more robust network structures.

Complex networks are the preferential framework to model spreading dynamics in several real-world complex systems. Complex networks can describe the contacts between infectious individuals, responsible for disease spreading in real-world systems. Understanding how the network structure affects an epidemic outbreak is therefore of great importance to evaluate the vulnerability of a network and optimize disease control. Here we argue that the best network structure indexes (NSIs) to predict the disease spreading extent in real-world networks are based on the notion of network node distance rather than on network connectivity as commonly believed. We numerically simulated, via a type-SIR model, epidemic outbreaks spreading on 50 real-world networks. We then tested which NSIs, among 40, could a priori better predict the disease fate. We found that the "average normalized node closeness " and the "average node distance " are the best predictors of the initial spreading pace, whereas indexes of "topological complexity " of the network, are the best predictors of both the value of the epidemic peak and the final extent of the spreading. Furthermore, most of the commonly used NSIs are not reliable predictors of the disease spreading extent in real-world networks.

We compared seven node vaccination strategies in twelve real-world complex networks. The node vaccination strategies are modeled as node removal on networks. We performed node vaccination strategies both removing nodes according to the initial network structure, i.e., non-adaptive approach, and performing partial node rank recalculation after node removal, i.e., semi-adaptive approach. To quantify the efficacy of each vaccination strategy, we used three epidemic spread indicators: the size of the largest connected component, the total number of infected at the end of the epidemic, and the maximum number of simultaneously infected individuals. We show that the best vaccination strategies in the non-adaptive and semi-adaptive approaches are different and that the best strategy also depends on the number of available vaccines. Furthermore, a partial recalculation of the node centrality increases the efficacy of the vaccination strategies by up to 80%.

In this article, we implement and compare 10 node removal (attack) strategies from the literature over the photosystem I (PSI) complex network of the common pea plant (Pisum sativum), representing the FRET energy transfer among its nodes/chromophores. We measure the network robustness (functioning) with four indicators. The node attack strategies and the network robustness indicators consider both the binary-topological and the weighted structure of the network. First, we find that the well-known node betweenness centrality attack, which has proven highly effective in dismantling most real-world networks’ topological connectivity, is ineffective over the PSI network. Second, the degeneracy of the node properties caused by the PSI’s higher network connectivity level induces a random-like node removal even when nodes are removed according to a specific node centrality measure. This phenomenon triggers a very low decrease of the PSI network functioning even when subjected to node attack. Such an outcome would indicate that the node attack strategies based on classic node properties, such as the degree or the betweenness centrality, may show low efficacy in dismantling real-world networks with very high connectivity levels. Last, the PSI network can be built by tuning a cut-off distance (CD) that defines the viable energy transfers among nodes/chromophores and progressively discards the lower energy transfer links among distant nodes/chromophores. This represents a ‘weight thresholding’ procedure allowing us to investigate the efficacy of the node attack strategies when links of lower weight are progressively pruned from the PSI network. We find that the best node attack strategies change by decreasing the CD, showing that the weight thresholding procedure affects the network response to node removal. This last outcome outlines the importance of investigating the stability of the system response for real-world weighted complex networks subjected to the weight thresholding procedure.

We model the COVID-19 spreading by running SIR Monte-Carlo simulations in four real face-to-face contact networks. We evaluate the effectiveness of the ‘facemask use’ and ‘vaccination policies’ to curb epidemic spreading. We model the facemask use policy by assuming a lower individual infection probability $\beta$ . We found that while this strategy can delay the disease spreading, it does not significantly reduce the total number of infected individuals (TI), as 80% of the total population still is infected at the end of the epidemic. We model vaccination by setting individual's infection probability $\beta=0$ , which is equivalent to remove nodes/individuals from the network. The vaccination was found to be very effective. Even with a partial vaccination of 30% of the population nodes selected considering their centrality measure ranking, such as degree, betweenness, or PageRank, it was possible to reduce the TI of 14%. Finally, yet importantly, random partial vaccination is not effective at all, meaning that most of the unvaccinated population will be infected.

Computing the robustness of a network, i.e., the capacity of a network holding its main functionality when a proportion of its nodes/edges are damaged, is useful in many real applications. The Monte Carlo numerical simulation is the commonly used method to compute network robustness. However, it has a very high computational cost, especially for large networks. Here, we propose a methodology such that the robustness of large real-world social networks can be predicted using machine learning models, which are pretrained using existing datasets. We demonstrate this approach by simulating two effective node attack strategies, i.e., the recalculated degree (RD) and initial betweenness (IB) node attack strategies, and predicting network robustness by using two machine learning models, multiple linear regression (MLR) and the random forest (RF) algorithm. We use the classic network robustness metric R as a model response and 8 network structural indicators (NSI) as predictor variables and trained over a large dataset of 48 real-world social networks, whose maximum number of nodes is 265,000. We found that the RF model can predict network robustness with a mean squared error (RMSE) of 0.03 and is 30% better than the MLR model. Among the results, we found that the RD strategy has more efficacy than IB for attacking real-world social networks. Furthermore, MLR indicates that the most important factors to predict network robustness are the scale-free exponent α and the average node degree . On the contrary, the RF indicates that degree assortativity a, the global closeness, and the average node degree are the most important factors. This study shows that machine learning models can be a promising way to infer social network robustness.

Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent—but isolated—counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.