Ollin D. Langle-Chimal, Steffen Knoblauch & Marta C. González 
Nature Communications (2026)

Human mobility in urban areas largely depends on the spatial distribution of jobs and who pursues them, yet how workers balance proximity against economic opportunity remains poorly understood. Existing mechanistic models capture physically interpretable effects such as distance decay, but overlook how socioeconomic factors shape commuting decisions. We present WorkReach, a model grounded in discrete choice theory that embeds informality and economic complexity into a utility function and represents commuting as the outcome of workers behaving as if maximizing it. Applied to four cities in the United States, Mexico, and Brazil, it reproduces commuting flows as accurately as widely used benchmarks while making the underlying choices interpretable. Here, we show that workers consistently commute farther to economically sophisticated areas, while the role of informality differs across regions, and that measuring accessibility by the perceived benefit of opportunities, not just physical proximity, highlights disparities conventional metrics overlook.

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Fabiane de Fatima Carvalho, Ivan Bergier, Silvia Maria Fonseca Silveira Massruhá, Jayme Garcia Arnal Barbedo
Complexities 2026, 2(3), 21

Collaboration networks are frequently studied as empirical instances of complex social systems, yet standardized methodological frameworks for consistently identifying heterogeneous mesoscopic structural regimes remain limited. This study proposes an integrated multi-criteria classification framework and demonstrates its application to the structural characterization of communities extracted from a large-scale scientific collaboration network. The framework combines community detection, classical network metrics, statistical modeling of weighted degree tails, small-world diagnostics, information-entropy measures, and fractal analysis based on the Song–Havlin–Makse box-covering renormalization framework. As an empirical application, the methodology is applied to the giant coauthorship component of Embrapa’s scientific production (1974–2024), derived from the Brazilian Agricultural Research Database (BDPA), comprising 60,636 nodes. The weighted Louvain algorithm partitions the network into 25 major communities, which are evaluated through an integrated classification protocol combining the Akaike Information Criterion model selection, Kolmogorov–Smirnov goodness-of-fit tests, small-worldness diagnostics, and fractal scaling analysis. The proposed framework identifies three network families, namely Barabási–Albert (BA-like)/scale-free small-world, scale-free fractal (non-BA) and small-world (non-scale-free), while explicitly distinguishing supported and ambiguous classifications according to the overall consistency of the statistical and structural evidence. The results demonstrate that distinct mesoscopic structural regimes coexist within the same connected collaboration system, highlighting the usefulness of the proposed reproducible multi-criteria framework for comparative topological characterization across complex collaboration networks.Collaboration networks are frequently studied as empirical instances of complex social systems, yet standardized methodological frameworks for consistently identifying heterogeneous mesoscopic structural regimes remain limited. This study proposes an integrated multi-criteria classification framework and demonstrates its application to the structural characterization of communities extracted from a large-scale scientific collaboration network. The framework combines community detection, classical network metrics, statistical modeling of weighted degree tails, small-world diagnostics, information-entropy measures, and fractal analysis based on the Song–Havlin–Makse box-covering renormalization framework. As an empirical application, the methodology is applied to the giant coauthorship component of Embrapa’s scientific production (1974–2024), derived from the Brazilian Agricultural Research Database (BDPA), comprising 60,636 nodes. The weighted Louvain algorithm partitions the network into 25 major communities, which are evaluated through an integrated classification protocol combining the Akaike Information Criterion model selection, Kolmogorov–Smirnov goodness-of-fit tests, small-worldness diagnostics, and fractal scaling analysis. The proposed framework identifies three network families, namely Barabási–Albert (BA-like)/scale-free small-world, scale-free fractal (non-BA) and small-world (non-scale-free), while explicitly distinguishing supported and ambiguous classifications according to the overall consistency of the statistical and structural evidence. The results demonstrate that distinct mesoscopic structural regimes coexist within the same connected collaboration system, highlighting the usefulness of the proposed reproducible multi-criteria framework for comparative topological characterization across complex collaboration networks.

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Sean P. Maley, Carlos Gershenson, Stuart A. Kauffman

Journal of Theoretical Biology

How new levels of organization arise is a long-standing question. The emergence of higher-level organization can appear unlikely, since cooperation must prevail over competition. One well-studied example is the autocatalytic set, a collection of molecules in which the formation of each member is catalyzed by another member of the set, and which is often considered a prerequisite for the evolution of life.
We present a random threshold-directed network model that integrates node-specific traits with dynamic edge formation and node removal, simulating arbitrary levels of cooperation and competition. Intrinsic node values determine directed links through threshold rules, generating a multi-digraph with signed edges (reflecting support and antagonism, labeled “help” and “harm”) that yields two parallel yet interdependent threshold graphs. Incorporating temporal growth and node turnover allows exploration of the evolution, adaptation, and potential collapse of communities.
We find that a strongly connected core assembles and persists even when antagonistic interactions predominate. Members are culled once incoming harm outweighs incoming help, so those that remain are helped more than they are harmed, and a quantitative increase in the number of elements produces a qualitative transition. As the harm-to-help ratio ρ rises, late-time population growth and mean connectivity both decline steadily, growth reaching zero and connectivity its floor near ρc ≈ 0.6, marking a shift from sustained growth to a bounded regime. Raising the binding chance moves the onset of a system-spanning strongly connected component to progressively smaller populations without changing its eventual extent, indicating that interaction opportunity governs when collective organization appears rather than whether it appears.
These results extend classical random threshold and Erdős-Rényi random graph models, and bear on how microbial communities and other adaptive systems assemble Collective Affordance Sets under persistent antagonism.

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Klaus M. Frahm, Leonardo Ermann, and Dima L. Shepelyansky

Complexities 2026, 2(3), 20;

According to the recent Wealth Thermalization Hypothesis (WTH), the wealth inequality in the world is described by the Rayleigh–Jeans (RJ) thermal distribution of interacting agents in a society with social stratification. In this concept, the wealth layers of society are associated with energy levels from a nonlinear dynamical system conserving two integrals of motion—namely, total energy and the probability norm. This leads to RJ condensation and the formation of a huge poverty phase of low wealth and a tiny oligarchic phase that captures a main part of total society wealth. This RJ phenomenon has similarities with self-cleaning in multimode optical fibers and constraint-driven condensation in various physical systems. We analyze real Lorenz and Pareto curves for wealth of households in countries and the world; gross domestic product of countries; market capitalization of companies on the stock exchanges of Hong Kong, Shanghai, and London; bitcoin transactions; and world trade between countries and show that the WTH theory gives a good description of these curves. On the basis of this comparison, we argue that the RJ thermal distribution provides a universal description of wealth inequality in the world.

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