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Abstract Since its inception, the keystone species concept has become a central theoretical framework in ecology. Among many approaches, keystones have been operationalized in natural and human environments using centrality metrics applied to monolayer networks. Despite the great success of this approach, as species make several types of interactions, recent studies on keystones moved from monolayer to multilayer networks. To help fulfil the need for a centrality metric designed for multilayer networks, here we introduce Gnorm. We tested the performance of our new metric using in silico data in addition to an empirical data set of frugivory and nectarivory interactions between bats and plants in the Neotropics. A comparison between the results obtained with different random and scale‐free networks demonstrates the performance of our new metric. First, a modularity analysis based on the multilayer version of the Louvain algorithm enables the modules to be composed of nodes from different layers. Second, by setting the coupling parameter (ω) and the resolution parameter (γ), module identity changes gradually, from single‐ to multiple‐node modules and from mono‐ to multilayer composition. Third, we check the number of modules from different layers to which a node belongs (G) at different levels of ω and γ. Finally, by observing how average G decreases with ω and γ, it is possible to calculate Gnorm and detect which nodes are most resistant to change in these two parameters. Those resistant nodes are identified as central in the multilayer structure. After applying this new analysis to the bat–plant network, we observed that it identified a different set of potential keystone species compared to previous analyses performed separately for each layer or the aggregated network. In conclusion, our new metric opens a new way of operationalizing the keystone species concept in multilayer networks. It may help identify keystone species involved in different interaction types.

Abstract Autism is a multifaceted neurodevelopmental condition whose accurate diagnosis may be challenging because the associated symptoms and severity vary considerably. The wrong diagnosis can affect families and the educational system, raising the risk of depression, eating disorders, and self-harm. Recently, many works have proposed new methods for the diagnosis of autism based on machine learning and brain data. However, these works focus on only one pairwise statistical metric, ignoring the brain network organization. In this paper, we propose a method for the automatic diagnosis of autism based on functional brain imaging data recorded from 500 subjects, where 242 present autism spectrum disorder considering the regions of interest throughout Bootstrap Analysis of Stable Cluster map. Our method can distinguish the control group from autism spectrum disorder patients with high accuracy. Indeed the best performance provides an AUC near 1.0, which is higher than that found in the literature. We verify that the left ventral posterior cingulate cortex region is less connected to an area in the cerebellum of patients with this neurodevelopment disorder, which agrees with previous studies. The functional brain networks of autism spectrum disorder patients show more segregation, less distribution of information across the network, and less connectivity compared to the control cases. Our workflow provides medical interpretability and can be used on other fMRI and EEG data, including small data sets.

Rumors and information spreading emerge naturally from human-to-human interaction and have a growing impact on people’s lives due to increasing and faster access to information, whether trustworthy or not. The authors study the Maki–Thompson rumor model and its variation, revealing a phase transition and providing insights into the nature of this transition.

Abstract Countries become global leaders by controlling international and domestic transactions connecting geographically dispersed production stages. We model global trade as a multi-layer network and study its power structure by investigating the tendency of eigenvector centrality to concentrate on a small fraction of countries, a phenomenon called localization transition. We show that the market underwent a significant drop in power concentration precisely in 2007 just before the global financial crisis. That year marked an inflection point at which new winners and losers emerged and a remarkable reversal of leading role took place between the two major economies, the US and China. We uncover the hierarchical structure of global trade and the contribution of individual industries to variations in countries’ economic dominance. We also examine the crucial role that domestic trade played in leading China to overtake the US as the world’s dominant trading nation. There is an important lesson that countries can draw on how to turn early signals of upcoming downturns into opportunities for growth. Our study shows that, despite the hardships they inflict, shocks to the economy can also be seen as strategic windows countries can seize to become leading nations and leapfrog other economies in a changing geopolitical landscape.

Diseases and other contagion phenomena in nature and society can interact asymmetrically, such that one can benefit from the other, which in turn impairs the first, in analogy with predator-prey systems. Here, we consider two models for interacting diseaselike dynamics with asymmetric interactions and different associated time scales. Using rate equations for homogeneously mixed populations, we show that the stationary prevalences and phase diagrams of each model behave differently with respect to variations of the relative time scales. We also characterize in detail the regime where transient oscillations are observed, a pattern that is inherent to asymmetrical interactions but often ignored in the literature. Our results contribute to a better understanding of disease dynamics in particular, and interacting processes in general, and could provide interesting insights for real-world applications.

Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits nontrivial dynamical patterns—such as chimeras, explosive transitions, and asymmetry-induced synchronization—that were once observed only in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erdős-Rényi, and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized states and a multitude of solutions of a collective state we denominate as a breathing standing wave, which displays global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.

We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. We find that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. Our findings also illustrate the role of dynamical-structural correlations, where we allow a power-law network to dynamically behave as a homogeneous structure by an appropriate tuning of its recovery rates. Overall, our results demonstrate that heterogeneity in the recovery rates, eventually in all dynamical parameters, is as important as the structural heterogeneity.

The worldwide trade network has been widely studied through different data sets and network representations with a view to better understanding interactions among countries and products. Here we investigate international trade through the lenses of the single-layer, multiplex, and multi-layer networks. We discuss differences among the three network frameworks in terms of their relative advantages in capturing salient topological features of trade. We draw on the World Input-Output Database to build the three networks. We then uncover sources of heterogeneity in the way strength is allocated among countries and transactions by computing the strength distribution and entropy in each network. Additionally, we trace how entropy evolved, and show how the observed peaks can be associated with the onset of the global economic downturn. Findings suggest how more complex representations of trade, such as the multi-layer network, enable us to disambiguate the distinct roles of intra- and cross-industry transactions in driving the evolution of entropy at a more aggregate level. We discuss our results and the implications of our comparative analysis of networks for research on international trade and other empirical domains across the natural and social sciences.

Though introduced recently, complex networks research has grown steadily because of its potential to represent, characterize and model a wide range of intricate natural systems and phenomena. Because of the intrinsic complexity and systemic organization of life, complex networks provide a specially promising framework for systems biology investigation. The current article is an up-to-date review of the major developments related to the application of complex networks in biology, with special attention focused on the more recent literature. The main concepts and models of complex networks are presented and illustrated in an accessible fashion. Three main types of networks are covered: transcriptional regulatory networks, protein-protein interaction networks and metabolic networks. The key role of complex networks for systems biology is extensively illustrated by several of the papers reviewed.

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible–infected–recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation.

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.