Random Walks on Multiplex Networks

Abstract

Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks under random failures", we extend well-known random walks to multiplexes and we introduce a new type of walk that can exist only in multiplexes. We derive exact expressions for vertex occupation time and the coverage. Finally, we show how the efficiency in exploring the multiplex critically depends on the underlying topology of layers, the weight of their inter-connections and the strategy adopted to walk.

10 pages, 8 figures, 5 tables, Supplementary material for the paper "Navigability of interconnected networks under random failures" (http://www.pnas.org/content/early/2014/05/21/1318469111.abstract)

References in corpus (10)

• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• First-passage times in complex scale-invariant media
• Abrupt transition in the structural formation of interconnected networks
• Spectral coarse-graining of complex networks
• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
• Maximal-entropy random walks in complex networks with limited information
• Exploring Complex Networks through Random Walks
• From the Physics of Interacting Polymers to Optimizing Routes on the London Underground
• Random Walks on Complex Networks

Cited by in corpus (156)

• Multilayer Networks
• Human Mobility: Models and Applications
• Random walks and diffusion on networks
• The physics of spreading processes in multilayer networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Predicting multicellular function through multi-layer tissue networks
• Centrality in Interconnected Multilayer Networks
• MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
• Measuring and modelling correlations in multiplex networks
• Spreading processes in Multilayer Networks
• Percolation in Multiplex Networks with Overlap
• Percolation in real interdependent networks
• Random walks on hypergraphs
• Network Geometry
• Multiplex PageRank
• Representing higher-order dependencies in networks
• Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
• Master stability functions for complete, intra-layer and inter-layer synchronization in multiplex networks
• Multiple percolation transitions in a configuration model of network of networks
• The Multilayer Temporal Network of Public Transport in Great Britain
• Congestion induced by the structure of multiplex networks
• Spectral entropies as information-theoretic tools for complex network comparison
• Towards real-world complexity: an introduction to multiplex networks
• Mapping multiplex hubs in human functional brain network
• A multilayer perspective for the analysis of urban transportation systems
• Hidden geometric correlations in real multiplex networks
• Structure of Triadic Relations in Multiplex Networks
• Multiplex lexical networks reveal patterns in early word acquisition in children
• Redundant interdependencies boost the robustness of multilayer networks
• Think Locally, Act Locally: The Detection of Small, Medium-Sized, and Large Communities in Large Networks
• Symmetries and Cluster Synchronization in Multilayer Networks
• Complex Networks from Classical to Quantum
• Random walk centrality in interconnected multilayer networks
• Optimal percolation on multiplex networks
• Centralities of Nodes and Influences of Layers in Large Multiplex Networks
• Bond percolation on multiplex networks
• Multilayer stochastic block models reveal the multilayer structure of complex networks
• Multimodal urban mobility and multilayer transport networks
• Irreducibility of multilayer network dynamics: the case of the voter model
• Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights
• Functional Multiplex PageRank
• Node and layer eigenvector centralities for multiplex networks
• Recent advances of percolation theory in complex networks
• Quantifying layer similarity in multiplex networks: a systematic study
• Non-linear growth and condensation in multiplex networks
• Cover time for random walks on arbitrary complex networks
• Spatio-temporal networks: reachability, centrality and robustness
• Efficient exploration of multiplex networks
• From the origin of life to pandemics: Emergent phenomena in complex systems
• Multilink Communities of Multiplex Networks
• The interdependent network of gene regulation and metabolism is robust where it needs to be
• Mutually connected component of network of networks with replica nodes
• Epidemic spreading and bond percolation in multilayer networks
• Several Multiplexes in the same City: The role of wealth differences in urban mobility
• Mobility and Congestion in Dynamical Multilayer Networks with Finite Storage Capacity
• MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach
• Diffusion geometry unravels the emergence of functional clusters in collective phenomena
• Diffusion Dynamics and Optimal Coupling in Directed Multiplex Networks
• A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks
• Strategy for stopping failure cascades in interdependent networks
• Clustering determines the dynamics of complex contagions in multiplex networks
• Multilayer Network Science: from Cells to Societies
• Exact Coupling Threshold for Structural Transition in Interconnected Networks
• Growing Multiplex Networks with Arbitrary Number of Layers
• Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
• Targeted Damage to Interdependent Networks
• Social contagions with communication channels alternation on multiplex networks
• Diffusive behavior of multiplex networks
• Enhancing transport properties in interconnected systems without altering their structure
• Effect of shortest path multiplicity on congestion of multiplex networks
• Effects of temporal correlations in social multiplex networks
• Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem
• Multilayer patent citation networks: A comprehensive analytical framework for studying explicit technological relationships
• Levy random walks on multiplex networks
• The robustness of interdependent networks under the interplay between cascading failures and virus propagation
• Optimal transport in multilayer networks for traffic flow optimization
• Diffusion geometry of multiplex and interdependent systems
• Correlated network of networks enhances robustness against catastrophic failures
• Multilayer coevolution dynamics of the nonlinear voter model
• Interevent time distributions of human multi-level activity in a virtual world
• Interconnections between networks act like an external field in first-order percolation transitions
• Scaling in the recovery of urban transportation systems from special events
• Layer-layer competition in multiplex complex networks
• Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks
• Abrupt transition due to non-local cascade propagation in multiplex systems
• Multiple abrupt phase transitions in urban transport congestion
• k-core percolation on interdependent and interconnected multiplex networks
• Universal exploration dynamics of random walks
• Community detection in multiplex networks using locally adaptive random walks
• A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks
• Classical and quantum random-walk centrality measures in multilayer networks
• Synchronized and mixed outbreaks of coupled recurrent epidemics
• Nonlocal PageRank
• On the stability of network indices defined by means of matrix functions
• A Perron-Frobenius theory for block matrices associated to a multiplex network
• Sustainable optimal transport in multilayer networks
• Anatomy and efficiency of urban multimodal mobility
• Sizing the length of complex networks
• Opinion-Based Centrality in Multiplex Networks: A Convex Optimization Approach
• Information transfer in community structured multiplex networks
• mGNN: Generalizing the Graph Neural Networks to the Multilayer Case
• Zoo Guide to Network Embedding
• Extracting the multimodal fingerprint of urban transportation networks
• Cycles and Clustering in Multiplex Networks
• Link overlap influences opinion dynamics on multiplex networks: spin model approach
• Taming Chimeras in Networks through Multiplexing Delays
• Reconstruction of multiplex networks via graph embeddings
• Hyper-diffusion on multiplex networks
• Multiplex Markov Chains: Convection Cycles and Optimality
• Fractional dynamics on circulant multiplex networks: optimal coupling and long-range navigation for continuous-time random walks
• Nonlinear random walks optimize the trade-off between cost and prevention in epidemics lockdown measures : the ESIR model
• An ensemble perspective on multi-layer networks
• Random graphs and real networks with weak geometric coupling
• The Role of Multiplex Network Structure in Cooperation through Generalized Reciprocity
• Multiple structural transitions in interacting networks
• Self-segregation in heterogeneous metapopulation landscapes
• A link model approach to identify congestion hotspots
• Multiplex reconstruction with partial information
• Vulnerable Connectivity Caused by Local Communities in Spatial Networks
• Reconstructing Sparse Multiplex Networks with Application to Covert Networks
• Observability transition in multiplex networks
• A New Community Definition For MultiLayer Networks And A Novel Approach For Its Efficient Computation
• Quantifying navigation complexity in transportation networks
• Information measures and cognitive limits in multilayer navigation
• MultiAspect Graphs: Algebraic representation and algorithms
• Structure-Preserving Community In A Multilayer Network: Definition, Detection, And Analysis
• Patterns of Multiplex Layer Entanglement across Real and Synthetic Networks
• Sequential locality of graphs and its hypothesis testing
• Indirect Influence on Network Diffusion
• Deep Learning Super-Diffusion in Multiplex Networks
• SimBins: An information-theoretic approach to link prediction in real multiplex networks
• Structural prediction of super-diffusion in multiplex networks
• Weak nodes detection in urban transport systems: Planning for resilience in Singapore
• Systematic assessment of the quality of fit of the stochastic block model for empirical networks
• A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks
• Information Cocoons in Online Navigation
• Fluctuations of a surface relaxation model in interacting scale free networks
• Extracting Spatiotemporal Demand for Public Transit from Mobility Data
• Identifying Central Nodes in Multiplex Networks by Embracing Layer-Specific Heterogeneity via DomiRank
• Non-equilibrium random walks on multiplex networks
• Analysing Motifs in Multilayer Networks
• Making a Case for MLNs for Data-Driven Analysis: Modeling, Efficiency, and Versatility
• Dynamical leaps due to microscopic changes in multiplex networks
• Influence Robustness of Nodes in Multiplex Networks against Attacks
• Rock-Paper-Scissors Random Walks on Temporal Multilayer Networks
• A hybrid multiscale coarse-grained method for dynamics on complex networks
• Phase Synchronization on Spacially Embeded Duplex Networks with Total Cost Constraint
• Thematic recommendations on knowledge graphs using multilayer networks
• Maximizing the algebraic connectivity in multilayer networks with arbitrary interconnections
• Prime stars multiplexes
• An Efficient Framework for Computing Structure- And Semantics-Preserving Community in a Heterogeneous Multilayer Network
• Multiplex Networks with Intrinsic Fitness: Modeling the Merit-Fame Interplay via Latent Layers
• Random Matrix Analysis of Multiplex Networks
• Explainable, automated urban interventions to improve pedestrian and vehicle safety
• Cooperation dynamics of generalized reciprocity on complex networks
• Discrimination universally determines reconstruction of multiplex networks