Multilayer Networks

Abstract

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.

Working paper; 59 pages, 8 figures

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• Analysis of node2vec random walks on networks
• Higher-Order Networks Representation and Learning: A Survey
• Close and ordinary social contacts: how important are they in promoting large-scale contagion?
• Layer reconstruction and missing link prediction of multilayer network with a Maximum A Posteriori estimation
• Percolation of Hierarchical Networks and Networks of Networks
• A Mean-Field Approach to Evolving Spatial Networks, with an Application to Osteocyte Network Formation
• Synchronization scenarios in three-layer networks with a hub
• Orientations and matrix function-based centralities in multiplex network analysis of urban public transport
• A Stochastic Block Model Approach for the Analysis of Multilevel Networks: an Application to the Sociology of Organizations
• Hierarchical Aggregations for High-Dimensional Multiplex Graph Embedding
• Harnessing functional segregation across brain rhythms as a means to detect EEG oscillatory multiplexing during music listening
• Optimal redundancy against disjoint vulnerabilities in networks
• Evolving network structure of academic institutions
• Symmetries and synchronization in multilayer random networks
• 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
• Multilayer Network Analysis: The Identification of Key Actors in a Sicilian Mafia Operation
• Link persistence and conditional distances in multiplex networks
• Suppressed epidemics in multi-relational networks
• Systems Applications of Social Networks
• Replicator dynamics with diffusion on multiplex networks
• Complex quantum network models from spin clusters
• Impacts of Physical-Layer Information on Epidemic Spreading in Cyber-Physical Networked Systems
• Emergent Network Modularity
• Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
• The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks
• Pareto optimality in multilayer network growth
• Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach
• Diffusion on hierarchical systems of weakly-coupled networks
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Algebraic analysis of multiple social networks with multiplex
• Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system
• Graph Product Multilayer Networks: Spectral Properties and Applications
• Dimension reduction of noisy interacting systems
• Spreading of localized attacks on spatial multiplex networks with a community structure
• Coevolution of relationship-driven cooperation under recommendation protocol on multiplex networks
• REACT: REActive resilience for critical infrastructures using graph-Coloring Techniques
• Inference of Demographic Attributes based on Mobile Phone Usage Patterns and Social Network Topology
• Containing rumors spreading on correlated multiplex networks
• Multilayer modeling of adoption dynamics in energy demand management
• Information transfer in community structured multiplex networks
• Disease spreading with social distancing: A prevention strategy in disordered multiplex networks
• Optimization of coupling and global collapse in diffusively coupled socio-ecological resource exploitation networks
• Deep-learning-aided dismantling of interdependent networks
• Interpretable Water Level Forecaster with Spatiotemporal Causal Attention Mechanisms
• Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions
• Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
• Sustainable Satellite Communications in the 6G Era: A European View for Multi-Layer Systems and Space Safety
• Asymmetric disease dynamics in multihost interconnected networks
• Filtering higher-order datasets
• Compressing network populations with modal networks reveals structural diversity
• Stylized facts in social networks: Community-based static modeling
• Effect of overlap on spreading dynamics on multiplex networks
• Spontaneous symmetry breaking and discontinuous phase transition for spreading dynamics in multiplex networks
• Cycles and Clustering in Multiplex Networks
• Ranking with multiple types of pairwise comparisons
• Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks
• Zoo Guide to Network Embedding
• Extracting the multimodal fingerprint of urban transportation networks
• Evolutionary dynamics of organised crime and terrorist networks
• Resilience in multiplex networks by addition of cross-repulsive links
• Modularity in Multilayer Networks using Redundancy-based Resolution and Projection-based Inter-Layer Coupling
• Non-Markovian random walks characterize network robustness to nonlocal cascades
• A multilayer, multi-timescale model approach for economic and frequency control in power grids
• Deep learning based parameter search for an agent based social network model
• Hyper-diffusion on multiplex networks
• Extraction and integration of genetic networks from short-profile omic datasets
• Influence of Information Blocking on the Spread of Virus in Multilayer Networks
• Link overlap influences opinion dynamics on multiplex networks: spin model approach
• A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models
• Echo chamber effects in signed networks
• Inference of Edge Correlations in Multilayer Networks
• Stochastic Solutions for Dense Subgraph Discovery in Multilayer Networks
• Environmentally extended input-output analysis in complex networks: a multilayer approach
• DyANE: Dynamics-aware node embedding for temporal networks
• Multilayer adaptive networks in neuronal processing
• Resilience by Structural Entrenchment: Dynamics of Single-Layer and Multiplex Networks Following Sudden Changes to Tie Costs
• Digital cities and the spread of COVID-19: characterizing the impact of non-pharmaceutical interventions in five cities in Spain
• Impact of random and targeted disruptions on information diffusion during outbreaks
• Spectral co-Clustering in Multi-layer Directed Networks
• The influence of a transport process on the epidemic threshold
• General theory for extended-range percolation on simple and multiplex networks
• An ensemble perspective on multi-layer networks
• Spacing ratio statistics of multiplex directed networks
• Spanning connectivity in a multilayer network and its relationship to site-bond percolation
• Derivative of a hypergraph as a tool for linguistic pattern analysis
• Multidimensional epidemic thresholds in diffusion processes over interdependent networks
• SciNoBo : A Hierarchical Multi-Label Classifier of Scientific Publications
• Detecting Hidden Layers from Spreading Dynamics on Complex Networks
• Multiplex Markov Chains: Convection Cycles and Optimality
• Role of bridge nodes in epidemic spreading: Different regimes and crossovers
• Optimizing synchronization in multiplex networks of phase oscillators
• Approximation methods for the stability of complete synchronization on duplex networks
• Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks
• Untangling the role of diverse social dimensions in the diffusion of microfinance
• Collective dynamics of random Janus oscillator networks
• Factor Network Autoregressions
• Layer degradation triggers an abrupt structural transition in multiplex networks
• Node-layer duality in networked systems
• Multiple structural transitions in interacting networks
• Fusing Modalities by Multiplexed Graph Neural Networks for Outcome Prediction in Tuberculosis
• Steady-state joint distribution for first-order stochastic reaction kinetics
• The Role of Multiplex Network Structure in Cooperation through Generalized Reciprocity
• Structured networks and coarse-grained descriptions: a dynamical perspective
• Rank-Refining Seed Selection Methods for Budget Constrained Influence Maximisation in Multilayer Networks under Linear Threshold Model
• Cooperator-driven and defector-driven punishments: How do they influence cooperation?
• Predicting transitions in cooperation levels from network connectivity
• A maximum entropy network reconstruction of macroeconomic models
• Generalized $k$-core pruning process on directed networks
• Hypergraphon Mean Field Games
• Modeling temporal hypergraphs
• Similarity matrix average for aggregating multiplex networks
• Multiplex reconstruction with partial information
• Robustness Assessment of Complex Networks using the Idle Network
• On limitations of uniplex networks for modeling multiplex contagion
• The Phantom Alignment Strength Conjecture: Practical use of graph matching alignment strength to indicate a meaningful graph match
• Optimizing spreading dynamics in interconnected networks
• Complexity and irreducibility of dynamics on networks of networks
• Stochastic Block Models are a Discrete Surface Tension
• Multiplex networks of musical artists: the effect of heterogeneous inter-layer links
• Network-theoretic modeling of fluid-structure interactions
• Phase diagram and metastability of the Ising model on two coupled networks
• Broadcasting solutions on networked systems of phase oscillators
• Spontaneous repulsion in the $A+B\to 0$ reaction on coupled networks
• Multilayer network analysis of nuclear reactions
• Effect of Burstiness on the Air Transportation System
• Observability transition in multiplex networks
• Generic Multilayer Network Data Analysis with the Fusion of Content and Structure
• Network interpolation
• Strategic energy flows in input-output relations: a temporal multilayer approach
• Multiple Partitioning of Multiplex Signed Networks: Application to European Parliament Votes
• Ecosystem-wide influences on pull request decisions: insights from NPM
• Random walk in degree space and the time-dependent Watts-Strogatz model
• Designing Optimal Multiplex Networks for Certain Laplacian Spectral Properties
• Flow-based Community Detection in Hypergraphs
• Multilayer networks describing interactions in urban systems: a digital twin of five cities in Spain
• Modeling resource consumption in the US air transportation system via minimum-cost percolation
• A network community detection method with integration of data from multiple layers and node attributes
• Structure-Preserving Community In A Multilayer Network: Definition, Detection, And Analysis
• Structural transition in interdependent networks with regular interconnections
• Time-dependent community structure in legislation cosponsorship networks in the Congress of the Republic of Peru
• Multilayer Modularity Belief Propagation To Assess Detectability Of Community Structure
• Dynamic models of gentrification
• Quantifying plasticity: a network-based framework linking structure to dynamical regimes
• Triadic percolation on multilayer networks
• Resilience of antagonistic networks with regard to the effects of initial failures and degree-degree correlations
• Evolution of correlated multiplexity through stability maximization
• Inter-layer Degree Correlations in Heterogeneously Growing Multiplex Networks
• Deep Learning Super-Diffusion in Multiplex Networks
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• From reductionism to realism: Holistic mathematical modelling for complex biological systems
• The role of conformity in opinion dynamics modelling with multiple social circles
• Functional brain networks: great expectations, hard times, and the big leap forward
• Discovering hidden layers in quantum graphs
• Hidden transition in multiplex networks
• Inference of time-ordered multibody interactions
• The treewidth and pathwidth of graph unions
• Eigenvector centrality for multilayer networks with dependent node importance
• Homogenization of Wasserstein gradient flows
• Patterns of Multiplex Layer Entanglement across Real and Synthetic 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
• Making a Case for MLNs for Data-Driven Analysis: Modeling, Efficiency, and Versatility
• Local phase transitions in a model of multiplex networks with heterogeneous degrees and inter-layer coupling
• Robust speech recognition using consensus function based on multi-layer networks
• On the effect of memory on the Prisoner's Dilemma game in correlated networks
• Network science approach for identifying disruptive elements of an airline
• Cops and Robbers on Multi-Layer Graphs
• Fixation dynamics on multilayer networks
• Structural prediction of super-diffusion in multiplex networks
• Brain functions emerge as thermal equilibrium states of the connectome
• Multilayer Network Analysis of European Regional Flows
• Relay synchronization and control of dynamics in multiplex networks with unidirectional inter layer coupling
• Identifying Central Nodes in Multiplex Networks by Embracing Layer-Specific Heterogeneity via DomiRank
• Estimating Social Effects with Randomized and Observational Network Data
• A Geometric Perspective for High-Dimensional Multiplex Graphs
• Dynamical leaps due to microscopic changes in multiplex networks
• Regression with Observational Multilayered Network Data
• Scalable Holistic Analysis of Multi-Source, Data-Intensive Problems Using Multilayered Networks
• A Perspective on the Ubiquity of Interaction Streams in Human Realm
• Approximating Spatial Distance Through Confront Networks: Application to the Segmentation of Medieval Avignon
• Six General Ecosystem Properties are more Intense in Biogeochemical Cycling Networks than Food Webs
• Effect of Perturbation and Topological Structure on Synchronization Dynamics in Multilayer Networks
• Hyperbolic embedding of multilayer networks
• Measuring Interlayer Dependence of Large Degrees in Multilayer Inhomogeneous Random Graphs
• Discriminative community detection for multiplex networks
• Uncovering the Local Hidden Community Structure in Social Networks
• Random Matrix Analysis of Multiplex Networks
• Prime stars multiplexes
• Consistent Tie-Strength Labeling for Multilayer Strong Triadic Closure
• Critical behaviors of cascading dynamics on multiplex two-dimensional lattices
• Cascading failures in anisotropic interdependent networks of spatial modular structures
• Graphlets in multilayer networks
• Spectral theory of weighted hypergraphs via tensors
• Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products
• Hypothesis testing for community structure in temporal networks using e-values
• From Spatial to Spectral: Network Renormalization via Dynamical Correlations
• Heterogeneous Network Topology Induces the Widom Line