Xiangyi Meng, Benjamin Piazza, Csaba Both, Baruch Barzel & Albert-László Barabási 

Nature volume 649, pages 315–322 (2026)

The brain’s connectome1,2,3 and the vascular system4 are examples of physical networks whose tangible nature influences their structure, layout and, ultimately, their function. The material resources required to build and maintain these networks have inspired decades of research into wiring economy, offering testable predictions about their expected architecture and organization. Here we empirically explore the local branching geometry of a wide range of physical networks, uncovering systematic violations of the long-standing predictions of wiring minimization. This leads to the hypothesis that predicting the true material cost of physical networks requires us to account for their full three-dimensional geometry, resulting in a largely intractable optimization problem. We discover, however, an exact mapping of surface minimization onto high-dimensional Feynman diagrams in string theory5,6,7, predicting that, with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimization. Specifically, surface minimization predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organization of physical networks across a wide range of application domains. Finally, we predict the existence of stable orthogonal sprouts, which are not only prevalent in real networks but also play a key functional role, improving synapse formation in the brain and nutrient access in plants and fungi.

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Giulia Fischetti, Anna Mancini, Giulio Cimini, Jessica T. Davis, Abby Leung, Alessandro Vespignani, Guido Caldarelli
Accurate representations of the World Air Transportation Network (WAN) are fundamental inputs to models of global mobility, epidemic risk, and infrastructure planning. However, high-resolution, real-time data on the WAN are largely commercial and proprietary, therefore often inaccessible to the research community. Here we introduce a generative model of the WAN that treats air travel as a stochastic process within a maximum-entropy framework. The model uses airport-level passenger flows to probabilistically generate connections while preserving traffic volumes across geographic regions. The resulting reconstructed networks reproduce key structural properties of the WAN and enable simulations of dynamic spreading that closely match those obtained using the real network. Our approach provides a scalable, interpretable, and computationally efficient framework for forecasting and policy design in global mobility systems.

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Maxime Lucas, Luca Gallo, Arsham Ghavasieh, Federico Battiston & Manlio De Domenico
Nature Communications , Article number: (2026)

Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks’ apparent superior descriptive power—compared to classical pairwise networks—comes with a much increased model complexity and computational cost, challenging their application. Consequently, it is of paramount importance to establish a quantitative method to determine when such a modeling framework is advantageous with respect to pairwise models, and to which extent it provides a valuable description of empirical systems. Here, we propose an information-theoretic framework, accounting for how structures affect diffusion behaviors, quantifying the entropic cost and distinguishability of higher-order interactions to assess their reducibility to lower-order structures while preserving relevant functional information. Empirical analyses indicate that some systems retain essential higher-order structure, whereas in some technological and biological networks it collapses to pairwise interactions. With controlled randomization procedures, we investigate the role of nestedness and degree heterogeneity in this reducibility process. Our findings contribute to ongoing efforts to minimize the dimensionality of models for complex systems.

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Linghang Sun, Yifan Zhang, Cristian Axenie, Margherita Grossi, Anastasios Kouvelas, Michail A. Makridis

Transportation Research Part B: Methodological

Volume 205, March 2026, 103386

Major cities worldwide experience problems with the performance of their road transportation networks, and the continuous increase in traffic demand presents a substantial challenge to the optimal operation of urban road networks and the efficiency of traffic control strategies. The operation of transportation systems is widely considered to display fragile property, i.e., the loss in performance increases exponentially with the linearly growing magnitude of disruptions. Meanwhile, the risk engineering community is embracing the novel concept of antifragility, enabling systems to learn from past events and exhibit improved performance under disruptions of previously unseen magnitudes. In this study, based on established traffic flow theory knowledge, namely the Macroscopic Fundamental Diagram (MFD), we first conduct a rigorous mathematical analysis to theoretically prove the fragile nature of road transportation networks. Subsequently, we propose a skewness-based indicator that can be readily applied to cross-compare the degree of fragility for different networks solely dependent on the MFD-related parameters. Finally, we implement a numerical simulation calibrated with real-world network data to bridge the gap between the theoretical proof and the practical operations, with results showing the reinforcing effect of higher-order statistics and stochasticity on the fragility of the networks. This work aims to demonstrate the fragile nature of road transportation networks and guide researchers towards adopting the methods of antifragile design for future networks and traffic control strategies.

Read the full article at: www.sciencedirect.com