Multiplex networks are generalized network structures that are able to describe networks in which the same set of nodes are connected by links that have different connotations. Multiplex networks are ubiquitous since they describe social, financial, engineering and biological networks as well. Extending our ability to analyze complex networks to multiplex network structures increases greatly the level of information that is possible to extract from Big Data. For these reasons characterizing the centrality of nodes in multiplex networks and finding new ways to solve challenging inference problems defined on multiplex networks are fundamental questions of network science. In this paper we discuss the relevance of the Multiplex PageRank algorithm for measuring the centrality of nodes in multilayer networks and we characterize the utility of the recently introduced indicator function $\widetildeΘ^{S}$ for describing their mesoscale organization and community structure. As working examples for studying these measures we consider three multiplex network datasets coming for social science.
Urban mobility increasingly relies on multimodality, combining the use of bicycle paths, streets, and rail networks. These different modes of transportation are well described by multiplex networks. Here we propose the overlap census method which extracts a multimodal profile from a city's multiplex transportation network. We apply this method to 15 cities, identify clusters of cities with similar profiles, and link this feature to the level of sustainable mobility of each cluster. Our work highlights the importance of evaluating all the transportation systems of a city together to adequately …
Many interesting real-world systems are represented as complex networks with multiple types of interactions and complicated dependency structures between layers. These interactions can be encoded as having a valence with positive links marking interactions such as trust and friendship and negative links denoting distrust or hostility. Extracting information from these negative interactions is challenging since standard topological metrics are often poor predictors of negative link formation, particularly across network layers. In this paper, we introduce a method based on mutual information wh…
Multiplex networks describe a large variety of complex systems, whose elements (nodes) can be connected by different types of interactions forming different layers (networks) of the multiplex. Multiplex networks include social networks, transportation networks or biological networks in the cell or in the brain. Extracting relevant information from these networks is of crucial importance for solving challenging inference problems and for characterizing the multiplex networks microscopic and mesoscopic structure. Here we propose an information theory method to extract the network between the lay…
We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multiplex networks. Then, we study its relevance for the analysis of real-world systems by studying a social multiplex where information flows using formal/informal channels and an air transportation system where the layers represent different air companies. Accordingly, the communicability, which is essential for the good performance of these complex systems, emerges at a systemic operation point in the multiplex where t…
The dissemination of information and the development of public opinion are essential elements of most social media platforms and are often described as distinct, man-made occurrences. However, what is often disregarded is the interdependence between these two phenomena. Information dissemination serves as the foundation for the formation of public opinion, while public opinion, in turn, drives the spread of information. In our study, we model the co-evolutionary relationship between information and public opinion on heterogeneous multiplex networks. This model takes into account a minority of …
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…
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…
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…
A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation for many real-world systems. However, due to a variety of potential factors, such as limited budget and equipment, or physical impossibility, multiplex data can be difficult to observe directly. Often, only partial information on the layer structure of the system is available, whereas the remaining information is in the form of a single-layer network. In this work, we face the problem of reconstructing the hidden multiplex structure of an aggregated network fro…
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…
The entities of real-world networks are connected via different types of connections (i.e. layers). The task of link prediction in multiplex networks is about finding missing connections based on both intra-layer and inter-layer correlations. Our observations confirm that that in a wide range of real-world multiplex networks, from social to biological and technological, a positive correlation exists between connection probability in one layer and similarity in other layers. Accordingly, a similarity-based automatic general-purpose multiplex link prediction method -- SimBins -- is devised that …
Betweenness centrality quantifies the importance of a vertex for the information flow in a network. We propose a flexible definition of betweenness for temporal multiplexes, where geodesics are determined accounting for the topological and temporal structure and the duration of paths. We propose an algorithm to compute the new metric via a mapping to a static graph. We show the importance of considering the temporal multiplex structure and an appropriate distance metric comparing the results with those obtained with static or single-layer metrics on a dataset of $\sim 20$k European flights.
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…
Exploiting the information about members of a Social Network (SN) represents one of the most attractive and dwelling subjects for both academic and applied scientists. The community of Complexity Science and especially those researchers working on multiplex social systems are devoting increasing efforts to outline general laws, models, and theories, to the purpose of predicting emergent phenomena in SN's (e.g. success of a product). On the other side the semantic web community aims at engineering a new generation of advanced services tailored to specific people needs. This implies defining con…
Many natural, engineered, and social systems can be represented using the framework of a layered network, where each layer captures a different type of interaction between the same set of nodes. The study of such multiplex networks is a vibrant area of research. Yet, understanding how to quantify the correlations present between pairs of layers, and more so present in their co-evolution, is lacking. Such methods would enable us to address fundamental questions involving issues such as function, redundancy and potential disruptions. Here we show first how the edge-set of a multiplex network can…
The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.). The mathematical description of these interacting networks has been coined under the name of multilayer networks, where each layer accounts for a type of interaction. It has been shown that diffusive processes on top of these networks present a phenomenology that cannot be explained by the naive superposi…
One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topolo…
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…
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…
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…
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…
In this paper, we study information transport in multiplex networks comprised of two coupled subnetworks. The upper subnetwork, called the logical layer, employs the shortest paths protocol to determine the logical paths for packets transmission, while the lower subnetwork acts as the physical layer, in which packets are delivered by the biased random walk mechanism characterized with a parameter $α$. Through simulation, we obtain the optimal $α$ corresponding to the maximum network lifetime and the maximum number of the arrival packets. Assortative coupling is better than the random coupling …
Until now, no simple symmetries have been detected in complex networks. Here we show that, in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglem…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics and statistics on these objects. We introduce a family of models of multiplex processes motivated by dynamical applications and investigate the properties of their spectra both theoretically and computationally. We study special cases of multiplex diffusion and Markov dynamics, using the spectral results to compute their rates of convergence. We use our frame…
We introduce a general method to infer the directional information flow between populations whose elements are described by n-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first extracting the network of genetic flow between the meadows of the seagrass Poseidonia Oceanica, where the meadow elements are specified by sets of microsatellite markers, then we extract the semantic flow network from a set of Wikipedia pages, showing the seman…
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…
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…
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 …
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, …
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…
Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous exposure to multiple sources of activation, called multiplex propagation, the effect of random links is just the opposite: it makes the propagation more difficult to achieve. We calculate analytical and numerically critical points for a threshold model in several classes of complex networks, including an empirical social network.
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also weighted, and the weights of the links can be strongly correlated with the structural properties of the multiplex network. For example in multiplex network formed by the citation and collaboration networks between PRE scientists it was found…
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…
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…
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system provides a qualitatively better model than the classical single-layer aggregated network. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we defin…
