Synergistic interactions are ubiquitous in the real world. Recent studies have revealed that, for a single-layer network, synergy can enhance spreading and even induce an explosive contagion. There is at the present a growing interest in behavior spreading dynamics on multiplex networks. What is the role of synergistic interactions in behavior spreading in such networked systems? To address this question, we articulate a synergistic behavior spreading model on a double layer network, where the key manifestation of the synergistic interactions is that the adoption of one behavior by a node in one layer enhances its probability of adopting the behavior in the other layer. A general result is that synergistic interactions can greatly enhance the spreading of the behaviors in both layers. A remarkable phenomenon is that the interactions can alter the nature of the phase transition associated with behavior adoption or spreading dynamics. In particular, depending on the transmission rate of one behavior in a network layer, synergistic interactions can lead to a discontinuous (first-order) or a continuous (second-order) transition in the adoption scope of the other behavior with respect to its transmission rate. A surprising two-stage spreading process can arise: due to synergy, nodes having adopted one behavior in one layer adopt the other behavior in the other layer and then prompt the remaining nodes in this layer to quickly adopt the behavior. Analytically, we develop an edge-based compartmental theory and perform a bifurcation analysis to fully understand, in the weak synergistic interaction regime where the dynamical correlation between the network layers is negligible, the role of the interactions in promoting the social behavioral spreading dynamics in the whole system.
Epidemic spreading on physical contact network will naturally introduce the human awareness information diffusion on virtual contact network, and the awareness diffusion will in turn depress the epidemic spreading, thus forming the competing spreading processes of epidemic and awareness in a multiplex networks. In this paper, we study the competing dynamics of epidemic and awareness, both of which follow the SIR process, in a two-layer networks based on microscopic Markov chain approach and numerical simulations. We find that strong capacities of awareness diffusion and self-protection of indi…
The numerous expanding online social networks offer fast channels for misinformation spreading, which could have a serious impact on socioeconomic systems. Researchers across multiple areas have paid attention to this issue with a view of addressing it. However, no systematical theoretical study has been performed to date on observing misinformation spreading on correlated multiplex networks. In this study, we propose a multiplex network-based misinformation spreading model, considering the fact that each individual can obtain misinformation from multiple platforms. Subsequently, we develop a …
A model for the spreading of online information or "memes" on multiplex networks is introduced and analyzed using branching-process methods. The model generalizes that of [Gleeson et al., Phys.Rev. X., 2016] in two ways. First, even for a monoplex (single-layer) network, the model is defined for any specific network defined by its adjacency matrix, instead of being restricted to an ensemble of random networks. Second, a multiplex version of the model is introduced to capture the behaviour of users who post information from one social media platform to another. In both cases the branching proce…
We study a model of information spreading on multiplex networks, in which agents interact through multiple interaction channels (layers), say online vs.\ offline communication layers, subject to layer-switching cost for transmissions across different interaction layers. The model is characterized by the layer-wise path-dependent transmissibility over a contact, that is dynamically determined dependently on both incoming and outgoing transmission layers. We formulate an analytical framework to deal with such path-dependent transmissibility and demonstrate the nontrivial interplay between the mu…
Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop …
Internet communication channels, e.g., Facebook, Twitter, and email, are multiplex networks that facilitate interaction and information-sharing among individuals. During brief time periods users often use a single communication channel, but then communication channel alteration (CCA) occurs. This means that we must refine our understanding of the dynamics of social contagions. We propose a non-Markovian behavior spreading model in multiplex networks that takes into account the CCA mechanism, and we develop a generalized edge-based compartmental method to describe the spreading dynamics. Throug…
In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact network), leading to the diffusion of awareness in the other network (information network), and then the diffusion of awareness will cause individuals to take social distances, which in turn affects the epidemic spreading. As for the diffusion of awareness, we assume that, on the one hand, individuals can be informed by other aware neighbors in information ne…
We present the analysis of the interrelation between two processes accounting for the spreading of an epidemics, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a Microscopic Markov Chain Approac…
Rumors flooding on rapidly-growing online social networks has geared much attention from many fronts. Individuals can transmit rumors via numerous channels since they can be active on multiple platforms. However, no systematic theoretical research of rumors containing dynamics on multiplex networks has been conducted yet. In this study, we propose a family of containing strategies based on the degree product $\mathcal{K}$ of each user on the multiplex networks. Then, we develop a heterogeneous edge-based compartmental theory to comprehend the containing dynamics. The simulation results demonst…
Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently mainly thanks to the development of multiplex and time-varying networks. However, these two advancements have progressed almost in parallel with very little overlap. Thus, the interplay between multiplexity and the temporal nature of connectivity patterns is poorly understood. Here, we aim to tackle this limitation by introducing a time-varying model of multiplex networks. We are interested in character…
A more connected world has brought major consequences such as facilitate the spread of diseases all over the world to quickly become epidemics, reason why researchers are concentrated in modeling the propagation of epidemics and outbreaks in Multilayer Networks. In this networks all nodes interact in different layers with different type of links. However, in many scenarios such as in the society, a Multiplex Network framework is not completely suitable since not all individuals participate in all layers. In this paper, we use a partially overlapped Multiplex Network where only a fraction of th…
Although there is always an interplay between the dynamics of information diffusion and disease spreading, the empirical research on the systemic coevolution mechanisms connecting these two spreading dynamics is still lacking. Here we investigate the coevolution mechanisms and dynamics between information and disease spreading by utilizing real data and a proposed spreading model on multiplex network. Our empirical analysis finds asymmetrical interactions between the information and disease spreading dynamics. Our results obtained from both the theoretical framework and extensive stochastic nu…
Network structure can have significant effects on the propagation of diseases, memes, and information on social networks. Such effects depend on the specific type of dynamical process that affects the nodes and edges of a network, and it is important to develop tractable models of spreading processes on networks to explore how network structure affects dynamics. In this paper, we incorporate the idea of \emph{synergy} into a two-state ("active" or "passive") threshold model of social influence on networks. Our model's update rule is deterministic, and the influence of each meme-carrying (i.e.,…
A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up "new ideas". Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas through "viral" influence spreading producing cascades of followers fragmenting an old network to create a new one. Typical examples include the raise of scientific ideas or abrupt changes in social media, like the raise of Facebook.com to the detriment of Myspace.com. How this process arises in practice has not been conclusively demonstrated. Here, we show …
Information diffusion and disease spreading in communication-contact layered network are typically asymmetrically coupled with each other, in which how an individual being aware of disease responds to the disease can significantly affect the disease spreading. Many recent studies have demonstrated that human behavioral adoption is a complex and non-Markovian process, where the probability of adopting one behavior is dependent on the cumulative times of the received information and the social reinforcement effect of these cumulative information. We study the impact of such a non-Markovian vacci…
Cooperation and competition between pathogens can alter the amount of individuals affected by a co-infection. Nonetheless, the evolution of the pathogens' behavior has been overlooked. Here, we consider a co-evolutionary model where the simultaneous spreading is described by a two-pathogen susceptible-infected-recovered model in an either synergistic or competitive manner. At the end of each epidemic season, the pathogens species reproduce according to their fitness that, in turn, depends on the payoff accumulated during the spreading season in a hawk-and-dove game. This co-evolutionary model …
Epidemic-like spreading processes on top of multilayered interconnected complex networks reveal a rich phase diagram of intertwined competition effects. A recent study by the authors [Granell et al. Phys. Rev. Lett. 111, 128701 (2013)] presented the analysis of the interrelation between two processes accounting for the spreading of an epidemics, and the spreading of information awareness to prevent its infection, on top of multiplex networks. The results in the case in which awareness implies total immunization to the disease, revealed the existence of a metacritical point at which the critica…
Comparing with single networks, the multiplex networks bring two main effects on the spreading process among individuals. First, the pathogen or information can be transmitted to more individuals through different layers at one time, which enlarges the spreading scope. Second, through different layers, an individual can also transmit the pathogen or information to the same individuals more than once at one time, which makes the spreading more effective. To understand the different roles of the spreading scope and effectiveness, we propose an epidemic model on multiplex networks with link overl…
We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a …
Identifying the most influential spreaders is important to understand and control the spreading process in a network. As many real-world complex systems can be modeled as multilayer networks, the question of identifying important nodes in multilayer network has attracted much attention. Existing studies focus on the multilayer network structure, while neglecting how the structural and dynamical coupling of multiple layers influence the dynamical importance of nodes in the network. Here we investigate on this question in an information-disease coupled spreading dynamics on multiplex networks. F…
In spite of the vast literature on spreading dynamics on complex networks, the role of local synergy, i.e., the interaction of elements that when combined produce a total effect greater than the sum of the individualelements, has been studied but only for irreversible spreading dynamics. Reversible spreading dynamics are ubiquitous but their interplay with synergy has remained unknown. To fill this knowledge gap, we articulate a model to incorporate local synergistic effect into the classical susceptible-infected-susceptible process, in which the probability for a susceptible node to become in…
Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must rely on resources from family or friends. We study the dynamics of disease spreading in social-contact multiplex networks when the recovery of infected nodes depends on resources from healthy neighbors in the social layer. We investigate how degree heterogeneity affects the spreading dynamics. Using theoretical analysis and simulations we find that degree heter…
This paper focuses on studying and understanding of stochastic dynamics in population composition when the population is subject to rumor spreading. We undertake the study by first developing an individual Susceptible-Exposed-Infectious-Removed (iSEIR) model, an extension of the SEIR model, for summarizing rumor-spreading behaviors of interacting groups in the population. With this iSEIR model, the interacting groups may be regarded as nodes in a multiplex network. Then various properties of the dynamic behaviors of the interacting groups in rumor spreading can be drawn from samples of the mul…
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbours, as introduced by Bagnoli et al., PRE 76:061904 (2007). We re-derive previous results using a self-organized method, that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by contacts in real life but…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is …
We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of th…
In spite of the study of epidemic dynamics on single-layer networks has received considerable attention, the epidemic dynamics on multiplex networks is still limited and is facing many challenges. In this work, we consider the susceptible-infected-susceptible-type (SIS) epidemic model on multiplex networks and investigate the effect of overlap among layers on the spreading dynamics. To do so, we assume that the prerequisite of one $S$-node to be infected is that there is at least one infectious neighbor in each layer. A remarkable result is that the overlap can alter the nature of the phase tr…
We study the effect of localized attacks on a multiplex spatial network, where each layer is a network of communities. The system is considered functional when the nodes belong to the giant component in all the multiplex layers. The communities are of linear size $ζ$, such that within them any pair of nodes are linked with same probability, and additionally nodes in nearby communities are linked with a different (typically smaller) probability. This model can represent an interdependent infrastructure system of cities where within the city there are many links while between cities there are fe…
Network ecology is a rising field of quantitative biology representing ecosystems as complex networks. A suitable example is parasite spreading: several parasites may be transmitted among their hosts through different mechanisms, each one giving rise to a network of interactions. Modelling these networked, ecological interactions at the same time is still an open challenge. We present a novel spatially-embedded multiplex network framework for modelling multi-host infection spreading through multiple routes of transmission. Our model is inspired by T. cruzi, a parasite transmitted by trophic an…
Identifying super-spreaders in epidemics is important to suppress the spreading of disease especially when the medical resource is limited.In the modern society, the information on epidemics transmits swiftly through various communication channels which contributes much to the suppression of epidemics. Here we study on the identification of super-spreaders in the information-disease coupled spreading dynamics. Firstly, we find that the centralities in physical contact layer are no longer effective to identify super-spreaders in epidemics, which is due to the suppression effects from the inform…
Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease --and its prevention methods-- using the unaware-aware-unaware dynamics, …
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thom…
The spread of behavior in a society has two major features: the synergy of multiple spreaders and the dominance of hubs. While strong synergy is known to induce mixed-order transitions (MOTs) at percolation, the effects of hubs on the phenomena are yet to be clarified. By analytically solving the generalized epidemic process on random scale-free networks with the power-law degree distribution $p_k \sim k^{-α}$, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for $α< 4$, an abundance of hubs drive MOTs, even if a synergistic spread…
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction $q$ of shar…
The spread of one disease, in some cases, can stimulate the spreading of another infectious disease. Here, we treat analytically a symmetric coinfection model for spreading of two diseases on a two-layer multiplex network. We allow layer overlapping, but we assume that each layer is random and locally loopless. Infection with one of the diseases increases the probability of getting infected with the other. Using the generating function method, we calculate exactly the fraction of individuals infected with both diseases (so-called coinfected clusters) in the stationary state, as well as the epi…
We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and for a given content (e.g., rumor, product, political view), each link type is associated with a content dependent parameter $c_i$ in $[0,\infty]$ that measures the relative bias type-$i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold τ. Namely, a node connected to $m_i$ active neighbors and $k_i-m_i$ inactive neighbors via type-$i$ …
Resource diffusion is an ubiquitous phenomenon, but how it impacts epidemic spreading has received little study. We propose a model that couples epidemic spreading and resource diffusion in multiplex networks. The spread of disease in a physical contact layer and the recovery of the infected nodes are both strongly dependent upon resources supplied by their counterparts in the social layer. The generation and diffusion of resources in the social layer are in turn strongly dependent upon the state of the nodes in the physical contact layer. Resources diffuse preferentially or randomly in this m…
We introduce a model to study the delicate relation between the spreading of information and the formation of opinions in social systems. For this purpose, we propose a two-layer multiplex network model in which consensus dynamics takes place in one layer while information spreading runs across the other one. The two dynamical processes are mutually coupled by considering that the control parameters that govern the dynamical evolution of the state of the nodes inside each layer depend on the dynamical states at the other layer. In particular, we explore the scenario in which consensus is favor…
Social reinforcement mechanism, which characterizes the promoting effects when exposing to multiple sources in social contagion process, is ubiquitous in information-technology ecosystem and has aroused great attention in recent years. While the impacts of social reinforcement on single-layer networks are well-documented, extension to multilayer networks is needed to study how reinforcement from different social circles influences the spreading dynamics. To this end, we incorporate multilayer social reinforcement into ignorant-spreader-ignorant (SIS) model on multiplex networks. Our theoretica…
We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with a biased diffusion process among different layers. A parameter $α$ is introduced to control the bias of the diffusion process, such that each individual prefers to move to one layer with more infected (or recovered) neighbors for larger values of $α$. Using stochastic simulations and mean-field theory, we show that the type of phase transition from a disease…
Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal percolation problem has direct applicability in strategies of immunization in disease spreading processes, and influence maximization for certain classes of opinion dynamical models. In this paper, we consider the problem of optimal percolation on multiplex networks. The multiplex scenario serves to realistically model various technological, biological, and social n…
We study the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter $r$, $r<1$ describes a moderate and committed society, for $r>1$ the society tends to have extremist opinions, w…
It has been recognized that many complex dynamical systems in the real world require a description in terms of multiplex networks, where a set of common, mutually connected nodes belong to distinct network layers and play a different role in each layer. In spite of recent progress towards data based inference of single-layer networks, to reconstruct complex systems with a multiplex structure remains largely open. We articulate a mean-field based maximum likelihood estimation framework to solve this outstanding and challenging problem. We demonstrate the power of the reconstruction framework an…
We develop a theoretical framework for the study of epidemic-like social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks. Specifically, we propose a contact-based information spreading model, and show that the critical point of the multiplex system associated to the active phase is determined by the layer whose contact probability matrix has the largest eigenvalue. The framework is applied to a number of different situations, including a real multiplex system. Finally, we also show th…
The impact of information dissemination on epidemic control is essentially subject to individual behaviors. Unlike information-driven behaviors, vaccination is determined by many cost-related factors, whose correlation with the information dissemination should be better understood. To this end, we propose an evolutionary vaccination game model in multiplex networks by integrating an information-epidemic spreading process into the vaccination dynamics, and explore how information dissemination influences vaccination. The spreading process is described by a two-layer coupled susceptible-alert-in…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application scenario is that commuters may adjust their behavior upon observing the symptoms and countermeasures from their physical contacts during travel, thus altering the trajectories of a disease outbreak. We introduce the heterogeneous mean-field (HMF) approach in a multiplex network setting to jointly model the spreading dynamics of the infectious disease in the cont…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers $M$. Specifically we propose and compare two message passing algorithms, that generalize the algorithm widely used to study the…
National stay-at-home orders, or lockdowns, were imposed in several countries to drastically reduce the social interactions mainly responsible for the transmission of the SARS-CoV-2 virus. Despite being essential to slow down the COVID-19 pandemic, these containment measures are associated with an economic burden. In this work, we propose a network approach to model the implementation of a partial lockdown, breaking the society into disconnected components, or partitions. Our model is composed by two main ingredients: a multiplex network representing human contacts within different contexts, f…
Opinion formation and disease spreading are among the most studied dynamical processes on complex networks. In real societies, it is expected that these two processes depend on and affect each other. However, little is known about the effects of opinion dynamics over disease dynamics and vice versa, since most studies treat them separately. In this work we study the dynamics of the voter model for opinion formation intertwined with that of the contact process for disease spreading, in a population of agents that interact via two types of connections, social and contact. These two interacting d…
The understanding and prediction of information diffusion processes on networks is a major challenge in network theory with many implications in social sciences. Many theoretical advances occurred due to stochastic spreading models. Nevertheless, these stochastic models overlooked the influence of rational decisions on the outcome of the process. For instance, different levels of trust in acquaintances do play a role in information spreading, and actors may change their spreading decisions during the information diffusion process accordingly. Here, we study an information-spreading model in wh…
In the early stage of epidemics, individuals' determination on adopting protective measures, which can reduce their risk of infection and suppress disease spreading, is likely to depend on multiple information sources and their mutual confirmation due to inadequate exact information. Here we introduce the inter-layer mutual confirmation mechanism into the information-disease interacting dynamics on multiplex networks. In our model, an individual increases the information transmission rate and willingness to adopt protective measures once he confirms the authenticity of news and severity of dis…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleadin…
University of Rome Tor Vergata（罗马托尔维尔加塔大学）；INFN（意大利国家核物理研究所）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB（交叉学科物理与复杂系统研究所（CSIC-UIB））；Univ. de Granada（格拉纳达大学）
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex systems and allow to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensem…
Many network contagion processes are inherently multiplex in nature, yet are often reduced to processes on uniplex networks in analytic practice. We therefore examine how data modeling choices can affect the predictions of contagion processes. We demonstrate that multiplex contagion processes are not simply the union of contagion processes over their constituent uniplex networks. We use multiplex network data from two different contexts -- (1) a behavioral network to represent their potential for infectious disease transmission using a "simple" epidemiological model, and (2) users from online …
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant inter-layer correlations -- degree-degree correlation, edge overlap, node similarities -- able to make them robust against random and targeted failures of their individual components. Here, we show that inter-layer correlations are important also in the characterization of their $\mathbf{…
