The structure and dynamics of multilayer networks

Abstract

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

arXiv commentIn Press, Accepted Manuscript, Physics Reports 2014

References in corpus (211)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Finding and evaluating community structure in networks
• Community detection in graphs
• Epidemic spreading in scale-free networks
• Lethality and centrality in protein networks
• Efficient Behavior of Small-World Networks
• Catastrophic cascade of failures in interdependent networks
• The architecture of complex weighted networks
• Statistical physics of social dynamics
• Functional cartography of complex metabolic networks
• Synchronization in complex networks
• Evolution of networks
• Mixing patterns in networks
• Evolutionary games on graphs
• Temporal Networks
• Network robustness and fragility: Percolation on random graphs
• Spatial Networks
• Characterization of complex networks: A survey of measurements
• Resilience of the Internet to random breakdowns
• Critical phenomena in complex networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Coevolutionary games - a mini review
• Epidemic dynamics and endemic states in complex networks
• Evolutionary prisoner's dilemma game on a square lattice
• Synchronization in small-world systems
• Breakdown of the Internet under intentional attack
• Evolutionary dynamics of group interactions on structured populations: A review
• Immunization of complex networks
• Efficient Immunization Strategies for Computer Networks and Populations
• Dynamical interplay between awareness and epidemic spreading in multiplex networks
• Diffusion dynamics on multiplex networks
• Recommender Systems
• The complex network of global cargo ship movements
• Multirelational Organization of Large-scale Social Networks in an Online World
• Mathematical Formulation of Multi-Layer Networks
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• An information-theoretic framework for resolving community structure in complex networks
• Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• Structural measures for multiplex networks
• Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
• Economic Small-World Behavior in Weighted Networks
• Communicability in complex networks
• Global organization of metabolic fluxes in the bacterium, Escherichia coli
• Robustness of a Network of Networks
• Voter Model on Heterogeneous Graphs
• The statistical mechanics of networks
• First-passage times in complex scale-invariant media
• Optimal network topologies for local search with congestion
• Discrete-time Markov chain approach to contact-based disease spreading in complex networks
• Fast Response and Temporal Coding on Coherent Oscillations in Small-World Networks
• Emergence of network features from multiplexity
• Mixture models and exploratory analysis in networks
• Suppressing cascades of load in interdependent networks
• Dynamical Organization of Cooperation in Complex Topologies
• Epidemic spreading in correlated complex networks
• Robustness of interdependent networks under targeted attack
• Interdependent network reciprocity in evolutionary games
• Efficiency of Scale-Free Networks: Error and Attack Tolerance
• The backbone of the climate network
• Robust Detection of Dynamic Community Structure in Networks
• Communication in networks with hierarchical branching
• Dynamics of Majority Rule
• Cascade of failures in coupled network systems with multiple support-dependent relations
• Layered Complex Networks
• Social consensus through the influence of committed minorities
• Voter Models on Heterogeneous Networks
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Avalanche Collapse of Interdependent Network
• Entropy measures for complex networks: Toward an information theory of complex topologies
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Heterogeneous aspirations promote cooperation in the prisoner's dilemma game
• Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies
• The Physics of Communicability in Complex Networks
• Evolution of public cooperation on interdependent networks: The impact of biased utility functions
• Abrupt transition in the structural formation of interconnected networks
• Localization and Spreading of Diseases in Complex Networks
• Epidemic spreading on interconnected networks
• Does a Single Zealot Affect an Infinite Group of Voters ?
• Growing multiplex networks
• Eigenvector centrality of nodes in multiplex networks
• Complex Networks as Hypergraphs
• Enhancing complex-network synchronization
• Optimal interdependence between networks for the evolution of cooperation
• Percolation Critical Exponents in Scale-Free Networks
• On the Role of Zealotry in the Voter Model
• Inter-similarity between coupled networks
• Spectral properties of the Laplacian of multiplex networks
• The extreme vulnerability of interdependent spatially embedded networks
• Modeling the Multi-layer Nature of the European Air Transport Network: Resilience and Passengers Re-scheduling under random failures
• The critical effect of dependency groups on the function of networks
• Threshold effects for two pathogens spreading on a network
• Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Transmission of Information and Herd Behavior: an Application to Financial Markets
• Generic Absorbing Transition in Coevolution Dynamics
• Contact-based Social Contagion in Multiplex Networks
• Modelling the Air Transport with Complex Networks: a short review
• Random hypergraphs and their applications
• Consensus formation on adaptive networks
• Multinetwork of international trade: A commodity-specific analysis
• Improved routing strategies for Internet traffic delivery
• Resilience to damage of graphs with degree correlations
• Network robustness of multiplex networks with interlayer degree correlations
• Competing epidemics on complex networks
• Degree mixing in multilayer networks impedes the evolution of cooperation
• Transport on coupled spatial networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Interdependent networks with correlated degrees of mutually dependent nodes
• Percolation in Multiplex Networks with Overlap
• A General Formalism for Inhomogeneous Random Graphs
• Dynamics of jamming transitions in complex networks
• Incomplete ordering of the voter model on small-world networks
• Robustness of a Tree-like Network of Interdependent Networks
• The entropy of randomized network ensembles
• Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks
• Rewarding evolutionary fitness with links between populations promotes cooperation
• Evolutionary dynamics on degree-heterogeneous graphs
• Stable Concurrent Synchronization in Dynamic System Networks
• Assessing the relevance of node features for network structure
• Assortativity Decreases the Robustness of Interdependent Networks
• Multiplexity-facilitated cascades in networks
• Multiplex PageRank
• Analytical maximum-likelihood method to detect patterns in real networks
• Identifying the Community Structure of the International-Trade Multi Network
• Percolation in Interdependent and Interconnected Networks: Abrupt Change from Second to First Order Transition
• Measuring social dynamics in a massive multiplayer online game
• Conservation laws for the voter model in complex networks
• Entropy Rate of Diffusion Processes on Complex Networks
• Multidimensional Social Network in the Social Recommender System
• Effect of the Interconnected Network Structure on the Epidemic Threshold
• Self-organization towards optimally interdependent networks by means of coevolution
• Synchronization in scale-free network with asymmetric coupling
• Temporal networks: slowing down diffusion by long lasting interactions
• Analysis of complex contagions in random multiplex networks
• Analytical results for the Sznajd model of opinion formation
• Conjoining Speeds up Information Diffusion in Overlaying Social-Physical Networks
• Efficient and exact sampling of simple graphs with given arbitrary degree sequence
• Percolation of Interdependent Networks with Inter-similarity
• Coevolution and correlated multiplexity in multiplex networks
• Heterogeneous believes, segregation and extremism in the making of public opinions
• Correlated multiplexity and connectivity of multiplex random networks
• Synchronization of interconnected networks: the role of connector nodes
• Congestion phenomena on complex networks
• Percolation of Partially Interdependent Scale-free Networks
• Information sharing promotes prosocial behaviour
• Exploring complex networks by walking on them
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Percolation in networks composed of connectivity and dependency links
• Modeling the dynamical interaction between epidemics on overlay networks
• Synchronization of hypernetworks of coupled dynamical systems
• Spreading of cooperative behaviour across interdependent groups
• Comparison of voter and Glauber ordering dynamics on networks
• Percolation of a general network of networks
• How women organize social networks different from men
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Network synchronization of groups
• Topology Induced Coarsening in Language Games
• Successful strategies for competing networks
• Multiple routes transmitted epidemics on multiplex networks
• Heterogeneous Voter Models
• The robustness of interdependent clustered networks
• Decelerating microdynamics can accelerate macrodynamics in the voter model
• Evolutionary Games defined at the Network Mesoscale: The Public Goods game
• Triple Point in Correlated Interdependent Networks
• Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
• Alignment and integration of complex networks by hypergraph-based spectral clustering
• Connect and win: The role of social networks in political elections
• Solution of voter model dynamics on annealed small-world networks
• Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
• Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
• Biased imitation in coupled evolutionary games in interdependent networks
• Are Percolation Transitions always Sharpened by Making Networks Interdependent?
• Hypergraph topological quantities for tagged social networks
• The Evolutionary Vaccination Dilemma in Complex Networks
• Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game
• Weak percolation on multiplex networks
• Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices
• Breathing synchronization in interconnected networks
• Triadic closure dynamics drives scaling-laws in social multiplex networks
• Stability of Boolean Multilevel Networks
• Analysis of Neighbourhoods in Multi-layered Dynamic Social Networks
• Spatial Scaling in Model Plant Communities
• Multiple resource demands and viability in multiplex networks
• Disentangling Social and Group heterogeneities: Public Goods games on Complex Networks
• Random Graphs with Hidden Color
• Percolation on interacting, antagonistic networks
• Voting and Catalytic Processes with Inhomogeneities
• Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks
• Dynamics of competing ideas in complex social systems
• Properties of Random Graphs with Hidden Color
• Early fragmentation in the adaptive voter model on directed networks
• Spatial Structure of the Internet Traffic
• Spreading of infectious diseases on heterogeneous populations: multi-type network approach
• Efficient routing on multilayered communication networks
• Constructing and sampling directed graphs with given degree sequences
• Stability of shortest paths in complex networks with random edge weights
• Majority-vote model on hyperbolic lattices
• Correlations between structure and dynamics in complex networks
• Sandpiles on multiplex networks
• Cavity-based robustness analysis of interdependent networks: Influences of intranetwork and internetwork degree-degree correlations
• Dynamics on Modular Networks with Heterogeneous Correlations
• Shortest Path Discovery in the Multi-layered Social Network
• Dynamical organization towards consensus in the Axelrod model on complex networks
• Dynamics of Vacillating Voters
• Topological Measure Locating the Effective Crossover between Segregation and Integration in a Modular Network
• Epidemic fronts in complex networks with metapopulation structure
• Effects of degree distribution in mutual synchronization of neural networks
• Phase transition in crowd synchrony of delay-coupled multilayer laser networks

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• Consensus ranking for multi-objective interventions in multiplex networks
• Synchronized and mixed outbreaks of coupled recurrent epidemics
• Vulnerability of state-interdependent networks under malware spreading
• Symmetry breaking in the prisoner's dilemma on two-layer dynamic multiplex networks
• Analysis of node2vec random walks on networks
• Layer reconstruction and missing link prediction of multilayer network with a Maximum A Posteriori estimation
• Harnessing functional segregation across brain rhythms as a means to detect EEG oscillatory multiplexing during music listening
• Optimal community structure for social contagions
• Close and ordinary social contacts: how important are they in promoting large-scale contagion?
• Orientations and matrix function-based centralities in multiplex network analysis of urban public transport
• Synchronization scenarios in three-layer networks with a hub
• Double transition of information spreading in a two-layered network
• Link persistence and conditional distances in multiplex networks
• Multilayer Network Analysis: The Identification of Key Actors in a Sicilian Mafia Operation
• Non-Markovian Majority-Vote model
• k-core structure of real multiplex networks
• Synchronization of wave structures in a heterogeneous multiplex network of 2D vdP lattices with attractive and repulsive intra-layer coupling
• Multiplex measures for higher-order networks
• Symmetries and synchronization in multilayer random networks
• Optimal redundancy against disjoint vulnerabilities in networks
• Suppressed epidemics in multi-relational networks
• A Perron-Frobenius theory for block matrices associated to a multiplex network
• Reference to Global State and Social Contagion Dynamics
• Emergent Network Modularity
• Counterpart synchronization of duplex networks with delayed nodes and noise perturbation
• Label propagation for clustering
• Impacts of Physical-Layer Information on Epidemic Spreading in Cyber-Physical Networked Systems
• Critical behavior of a two-step contagion model with multiple seeds
• Interacting social processes on interconnected networks
• Superconductor--Insulator Transition in a non-Fermi Liquid
• MultiNet: A Scalable Multilayer Network Embedding Framework
• The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks
• Impact of assortative mixing by mask-wearing on the propagation of epidemics in networks
• Effect of time varying transmission rates on coupled dynamics of epidemic and awareness over multiplex network
• Interplay of Delay and multiplexing: Impact on Cluster Synchronization
• Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
• Highly Clustered Complex Networks in the Configuration Model: Random Regular Small-World Network
• Spreading of localized attacks on spatial multiplex networks with a community structure
• A Novel Methodology for designing Policies in Mobile Crowdsensing Systems
• Spatial networks with wireless applications
• Pareto optimality in multilayer network growth
• Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach
• Graph Product Multilayer Networks: Spectral Properties and Applications
• Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system
• The effect of randomness for dependency map on the robustness of interdependent lattices
• Adversarial decision strategies in multiple network phased oscillators: the Blue-Green-Red Kuramoto-Sakaguchi model
• Dynamics of multilayer networks with amplification
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Koopman-based spectral clustering of directed and time-evolving graphs
• Percolation on spatial anisotropic networks
• Information transfer in community structured multiplex networks
• Disease spreading with social distancing: A prevention strategy in disordered multiplex networks
• Coevolution of relationship-driven cooperation under recommendation protocol on multiplex networks
• Containing rumors spreading on correlated multiplex networks
• Quenched mean-field theory for the majority-vote model on complex networks
• The topology of card transaction money flows
• Multilayer modeling of adoption dynamics in energy demand management
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Dynamics of "comb-of-comb" networks
• Algorithmic complexity of multiplex networks
• Quantum games of opinion formation based on the Marinatto-Weber quantum game scheme
• Mental Lexicon Growth Modelling Reveals the Multiplexity of the English Language
• Asymmetric disease dynamics in multihost interconnected networks
• Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions
• Effect of overlap on spreading dynamics on multiplex networks
• A practical method for estimating coupling functions in complex dynamical systems
• Mapping Coupled Time-series Onto Complex Network
• Stylized facts in social networks: Community-based static modeling
• Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
• Double phase transition of the Ising model in core-periphery networks
• Modularity in Multilayer Networks using Redundancy-based Resolution and Projection-based Inter-Layer Coupling
• Spontaneous symmetry breaking and discontinuous phase transition for spreading dynamics in multiplex networks
• Resilience in multiplex networks by addition of cross-repulsive links
• Zoo Guide to Network Embedding
• Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks
• Extracting the multimodal fingerprint of urban transportation networks
• Ranking with multiple types of pairwise comparisons
• Cycles and Clustering in Multiplex Networks
• Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles
• Evolutionary dynamics of organised crime and terrorist networks
• Deep learning based parameter search for an agent based social network model
• Hyper-diffusion on multiplex networks
• A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models
• Taming Chimeras in Networks through Multiplexing Delays
• Tipping induced by multiplexing on two layer networks
• Resilience by Structural Entrenchment: Dynamics of Single-Layer and Multiplex Networks Following Sudden Changes to Tie Costs
• Deterministic and stochastic cooperation transitions in evolutionary games on networks
• Reconstruction of multiplex networks via graph embeddings
• Extraction and integration of genetic networks from short-profile omic datasets
• Inference of Edge Correlations in Multilayer Networks
• SSNE: Effective Node Representation for Link Prediction in Sparse Networks
• Stochastic Solutions for Dense Subgraph Discovery in Multilayer Networks
• Link overlap influences opinion dynamics on multiplex networks: spin model approach
• A multilayer, multi-timescale model approach for economic and frequency control in power grids
• An ensemble perspective on multi-layer networks
• Approximation methods for the stability of complete synchronization on duplex networks
• Spacing ratio statistics of multiplex directed networks
• A quantum extension to inspection game
• Spanning connectivity in a multilayer network and its relationship to site-bond percolation
• The role of bipartite structure in R&D collaboration networks
• Multiplex Markov Chains: Convection Cycles and Optimality
• Statistical mechanics of bipartite $z$-matchings
• Detecting Hidden Layers from Spreading Dynamics on Complex Networks
• General theory for extended-range percolation on simple and multiplex networks
• Spectral co-Clustering in Multi-layer Directed Networks
• Multidimensional epidemic thresholds in diffusion processes over interdependent networks
• The influence of a transport process on the epidemic threshold
• Intertangled stochastic motifs in networks of excitatory-inhibitory units
• Percolation on Networks with Antagonistic and Dependent Interactions
• The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy
• Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks
• Derivative of a hypergraph as a tool for linguistic pattern analysis
• Enhanced robustness of single-layer networks with redundant dependencies
• Control of multidimensional systems on complex network
• Node-layer duality in networked systems
• Infection-induced Cascading Failures -- Impact and Mitigation
• Decoupling approximation robustly reconstructs directed dynamical networks
• Predicting transitions in cooperation levels from network connectivity
• Generalized $k$-core pruning process on directed networks
• Finite plateau in spectral gap of polychromatic constrained random networks
• Multiple structural transitions in interacting networks
• Structured networks and coarse-grained descriptions: a dynamical perspective
• Anomaly Detection of Complex Networks Based on Intuitionistic Fuzzy Set Ensemble
• Robust and Efficient Network Reconstruction in Complex System via Adaptive Signal Lasso
• Steady-state joint distribution for first-order stochastic reaction kinetics
• Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes
• Information transmission on hybrid networks
• Ferromagnetic transition in a simple variant of the Ising model on multiplex networks
• On limitations of uniplex networks for modeling multiplex contagion
• Multiplex reconstruction with partial information
• Geometric clusters in the overlap of the Ising model
• Information propagation in Gaussian processes on multilayer networks
• Modeling temporal hypergraphs
• Multiplex networks of musical artists: the effect of heterogeneous inter-layer links
• Steering complex networks toward desired dynamics
• Complexity and irreducibility of dynamics on networks of networks
• Triadic time series motifs
• Optimizing spreading dynamics in interconnected networks
• Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases
• Automatic exploration of structural regularities in networks
• Enhanced Quantum Transport in Multiplex Networks
• Two network Kuramoto-Sakaguchi model under tempered stable Lévy noise
• Can the PageRank centrality be manipulated to obtain any desired ranking?
• Sparse optimization of mutual synchronization in collectively oscillating networks
• Quantitative Discourse Cohesion Analysis of Scientific Scholarly Texts using Multilayer Networks
• Multilayer network analysis of nuclear reactions
• Observability transition in multiplex networks
• Interplay of inhibition and multiplexing : Largest eigenvalue statistics
• On Using Network Science in Mining Developers Collaboration in Software Engineering: A Systematic Literature Review
• Spontaneous repulsion in the $A+B\to 0$ reaction on coupled networks
• Node differentiation dynamics along the route to synchronization in complex networks
• Supporting novel biomedical research via multilayer collaboration networks
• Broadcasting solutions on networked systems of phase oscillators
• Time-dependent community structure in legislation cosponsorship networks in the Congress of the Republic of Peru
• Inter-layer Degree Correlations in Heterogeneously Growing Multiplex Networks
• Impacts of suppressing guide on information spreading
• Modeling resource consumption in the US air transportation system via minimum-cost percolation
• Teleportation fidelity of quantum repeater networks
• Evolution of correlated multiplexity through stability maximization
• Amplitude death in coupled replicator map lattice: averting migration dilemma
• Resilience of antagonistic networks with regard to the effects of initial failures and degree-degree correlations
• Synchronization in interacting Scale Free Networks
• The $q$-neighbor Ising model on multiplex networks with partial overlap of nodes
• Quantifying the temporal stability of international fertilizer trade networks
• Extractive Multi Document Summarization using Dynamical Measurements of Complex Networks
• Random walk in degree space and the time-dependent Watts-Strogatz model
• Triadic percolation on multilayer networks
• Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring
• Traveling phase waves in asymmetric networks of noisy chaotic attractors
• Disordered configurations of the Glauber model in two-dimensional networks
• Hidden transition in multiplex networks
• Deep Learning Super-Diffusion in Multiplex Networks
• Recovery of contour nodes in interdependent directed networks
• Inference of time-ordered multibody interactions
• Destroying Multicolored Paths and Cycles in Edge-Colored Graphs
• Epidemic risk perception and social interactions lead to awareness cascades on multiplex networks
• Discovering hidden layers in quantum graphs
• Improving J-divergence of brain connectivity states by graph Laplacian denoising
• Controlling Complex Systems
• Local phase transitions in a model of multiplex networks with heterogeneous degrees and inter-layer coupling
• Fixation dynamics on multilayer networks
• Spreader events and the limitations of projected networks for capturing dynamics on multipartite networks
• Fluctuations of a surface relaxation model in interacting scale free networks
• Multiple predator based capture process on complex networks
• Feature Learning and Network Structure from Noisy Node Activity Data
• Identifying Central Nodes in Multiplex Networks by Embracing Layer-Specific Heterogeneity via DomiRank
• Non-equilibrium random walks on multiplex networks
• On the effect of memory on the Prisoner's Dilemma game in correlated networks
• Estimating Social Effects with Randomized and Observational Network Data
• Herd Immunity with Spatial Adaptation Based on Global Prevalence Information
• Multilayer Network Analysis of European Regional Flows
• Dynamical leaps due to microscopic changes in multiplex networks
• Emergent togetherness in collaborative dance improvisation: neural and motor synchronization reveal a coupling-decoupling paradox
• Effect of Perturbation and Topological Structure on Synchronization Dynamics in Multilayer Networks
• Information diffusion in interconnected heterogeneous networks
• Multiplexity amplifies geometry in networks
• Mapping Inter-City Trade Networks to Maximum Entropy Models using Electronic Invoice Data
• BCI learning induces core-periphery reorganization in M/EEG multiplex brain networks
• Prime stars multiplexes
• From Spatial to Spectral: Network Renormalization via Dynamical Correlations
• Cooperative metabolic resource allocation in spatially-structured systems
• Modeling Epidemic Dynamics of Mutant Strains with Evolutionary Game-based Vaccination Behavior
• Graphlets in multilayer networks
• Edges of inter-layer synchronization in multilayer networks with time-switching links
• Heterogeneous Network Topology Induces the Widom Line
• Topological measures in weighted hypergraphs
• Cascading failures in anisotropic interdependent networks of spatial modular structures
• Multiplex Networks with Intrinsic Fitness: Modeling the Merit-Fame Interplay via Latent Layers
• Hidden multiscale organization and robustness of real multiplex networks
• Teleportation Fidelity of Binary Tree Quantum Repeater Networks
• Community Integration Algorithms (CIAs) for Dynamical Systems on Networks
• Trade-Off Between Multiplicity and Specificity in the Inter-layer Connectivity of non-identical Multilayer Networks
• Random Matrix Analysis of Multiplex Networks
• Consistent Tie-Strength Labeling for Multilayer Strong Triadic Closure
• Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products
• Regression with Observational Multilayered Network Data
• Hyperbolic embedding of multilayer networks