Alberto Aleta, Andreia Sofia Teixeira, Guilherme Ferraz de Arruda, Andrea Baronchelli, Alain Barrat, János Kertész, Albert Díaz-Guilera, Oriol Artime, Michele Starnini, Giovanni Petri, Márton Karsai, Siddharth Patwardhan, Alessandro Vespignani, Yamir Moreno, Santo Fortunato Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardized datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems. Read the full article at: arxiv.org

Guest Editors: Thiago B. Murari, Marcelo A. Moret, Hernane B. de B. Pereira, Tarcísio M. Rocha Filho, José F. F. Mendes, Tiziana Di Matteo Inspired by the Conference on Complex Systems 2023 (CCS2023) in Salvador, Brazil, this collection of EPJ B brings together 25 peer-reviewed articles covering a wide range of topics. This collection highlights the interdisciplinary nature of the field, with contributions from physics, biology, economics, linguistics, and artificial intelligence, and serves as a reference for researchers addressing real-world challenges through systems-based thinking. Read the full issue at: epjb.epj.org

Fernando Diaz-Diaz, Elena Candellone, Miguel A. Gonzalez-Casado, Emma Fraxanet, Antoine Vendeville, Irene Ferri, Andreia Sofia Teixeira Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This polarity reshapes how we think about structure and dynamics in complex systems: a negative tie is not simply a missing positive one but a constraint that generates tension, and possibly asymmetry. Across disciplines, from sociology to neuroscience and machine learning, signed networks provide a shared language to formalise duality, balance, and opposition as integral components of system behaviour. This review provides a comprehensive and foundational summary of signed network theory. It formalises the mathematical principles of signed graphs and surveys signed-network-specific measures, including signed degree distributions, clustering, centralities, motifs, and Laplacians. It revisits balance theory, tracing its cognitive and structural formulations and their connections to frustration. Structural aspects of signed networks are examined, analysing key topics such as null models, node embeddings, sign prediction, and community detection. Subsequent sections address dynamical processes on and of signed networks, such as opinion dynamics, contagion models, and data-driven approaches for studying evolving networks. Practical challenges in constructing, inferring and validating signed data from real-world systems are also highlighted, and we offer an overview of currently available datasets. We also address common pitfalls and challenges that arise when modelling or analysing signed data. Overall, this review integrates theoretical foundations, methodological approaches, and cross-domain examples, providing a structured entry point and a reference framework for researchers interested in the study of signed networks in complex systems. Read the full article at: arxiv.org

ALIFE 2025: Ciphers of Life: Proceedings of the Artificial Life Conference 2025 | October 2025 | Kyoto, Japan

The complex systems keyword diagram generated by the author in 2010 has been used widely in a variety of educational and outreach purposes, but it definitely needs a major update and reorganization. T...

Three of my PhD students are nearing completion of their final doctoral dissertation drafts, and

I remember a few years ago when I wrote a paper on debates around water

AI, trade wars and energy shifts aren’t separate stories

Alexander F. Siegenfeld and Yaneer Bar-Yam Entropy 2025, 27(8), 835 Ashby’s law of requisite variety allows a comparison of systems with their environments, providing a necessary (but not sufficient) condition for system efficacy: A system must possess at least as much complexity as any set of environmental behaviors that require distinct responses from the system. However, to account for the dependence of a system’s complexity on the level of detail—or scale—of its description, a multi-scale generalization of Ashby’s law is needed. We define a class of complexity profiles (complexity as a function of scale) that is the first, to our knowledge, to exhibit a multi-scale law of requisite variety. This formalism provides a characterization of multi-scale complexity and generalizes the law of requisite variety’s single constraint on system behaviors to a class of multi-scale constraints. We show that these complexity profiles satisfy a sum rule, which reflects a tradeoff between smaller- and larger-scale degrees of freedom, and we extend our results to subdivided systems and systems with a continuum of components. Read the full article at: www.mdpi.com

https://www.youtube.com/watch?v=Bp5aDgw9cOcWe welcome Carlos Gershenson to The Complexity Lounge. Carlos will propose that one of the main goals of science—the search for regularities in nature—points toward the concept of balance. He will discuss how complexity, evolution, criticality, and antifragility can be seen as resulting from different types of balance. The session will review specific mechanisms that promote balance, such as adaptation and self-organization, and conclude by exploring the philosophical implications of a worldview grounded in its scientific study. Watc at: www.youtube.com

At the frontiers of knowledge, researchers are discovering that A.I. doesn’t just take prompts—it gives them, too, sparking new forms of creativity and collaboration.

The aim of the school is to present methodological, computational and machine learning methods for complex networks analysis, with applications spanning a wide range of fields. The school will present a comprehensive view of the theoretical aspects of challenging topics in network theory, including higher order networks, diffusive models on networks, probabilistic and machine learning approaches, as well as computational methods. A wide range of applications will be explored during the lectures, including socio-economic and financial applications. A Python tutorial held by lecturers/teaching assistants will follow the lecture to show the implementation of the methods studied during the theoretical class and the proposed application. More at: tcn2025.wordpress.com

Every construction project implementation requires good project management, which aims to avoid or minimize project risks that may occur, including the risk of

César A. Hidalgo, Viktor Stojkoski Economic complexity estimates rely on eigenvectors derived from matrices of specialization to explain differences in economic growth, inequality, and sustainability. Yet, despite their widespread use, we still lack a principled theory that can deduce these eigenvectors from first principles and place them in the context of a mechanistic model. Here, we calculate these eigenvectors analytically for a model where the output of an economy in an activity increases with the probability the economy is endowed with the factors required by the activity. We show that the eigenvector known as the Economic Complexity Index or ECI is a monotonic function of the probability that an economy is endowed with a factor, and that in a multi-factor model, it is an estimate of the average endowment across all factors. We then generalize this result to other production functions and to a short-run equilibrium framework with prices, wages, and consumption. We find that our main result does not depend on the introduction of prices or wages, and that the derived wage function is consistent with the convergence of economies with a similar level of complexity. Finally, we use this model to explain the shape of networks of related activities, such as the product space and the research space. These findings solve long standing theoretical puzzles in the economic complexity literature and validate the idea that metrics of economic complexity are estimates of an economy being endowed with multiple factors. Read the full article at: arxiv.org

PyCX is a Python-based sample code repository for complex systems research and education. - hsayama/PyCX

The answer can come from an unexpected connection with the statistical physics of quantum systems

Nick and Peter wrote a book with the same title (Feedback). They discuss the similarities and differences between the two books. Feedback: How to Destroy and Save the World by Peter Erdi. Feedback: Uncovering the Hidden Connections between Life and the Universe by Nicholas Golledge. Watch/listen at: www.youtube.com