Structure of Triadic Relations in Multiplex Networks

Abstract

Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different "layers" that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks.

Main text + Supplementary Material included in a single file. Published in New Journal of Physics

References in corpus (34)

• Catastrophic cascade of failures in interdependent networks
• The architecture of complex weighted networks
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Intensity and coherence of motifs in weighted complex networks
• Dynamical interplay between awareness and epidemic spreading in multiplex networks
• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Mathematical Formulation of Multi-Layer Networks
• Structural measures for multiplex networks
• Generalizations of the clustering coefficient to weighted complex networks
• Robustness of a Network of Networks
• Random Walks on Multiplex Networks
• Suppressing cascades of load in interdependent networks
• Centrality in Interconnected Multilayer Networks
• Avalanche Collapse of Interdependent Network
• Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
• Eigenvector centrality of nodes in multiplex networks
• Inter-similarity between coupled networks
• Spectral properties of the Laplacian of multiplex networks
• Contact-based Social Contagion in Multiplex Networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks
• Multiplexity-facilitated cascades in networks
• Multiplex PageRank
• Formalising the multidimensional nature of social networks
• Analysis of complex contagions in random multiplex networks
• Percolation on interacting networks
• Are Percolation Transitions always Sharpened by Making Networks Interdependent?
• Stability of Boolean Multilevel Networks
• An ensemble approach to the analysis of weighted networks
• Analysis of Neighbourhoods in Multi-layered Dynamic Social Networks
• Preferential Attachment in the Interaction between Dynamically Generated Interdependent Networks

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• Visibility graphs for image processing
• Predicting future stock market structure by combining social and financial network information
• Clustering determines the dynamics of complex contagions in multiplex networks
• Multilayer Network Science: from Cells to Societies
• Complex networks with complex weights
• Prediction of scientific collaborations through multiplex interaction networks
• Link prediction in multiplex networks via triadic closure
• Multilayer network decoding versatility and trust
• Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization
• A tensor-based unified approach for clustering coefficients in financial multiplex networks
• Clustering coefficients as measures of the complex interactions in a directed weighted multilayer network
• Bridging Online and Offline Social Networks: Multiplex Analysis
• Cycles and Clustering in Multiplex Networks
• Sampling random graph homomorphisms and applications to network data analysis
• The role of bipartite structure in R&D collaboration networks
• Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
• Layer degradation triggers an abrupt structural transition in multiplex networks
• Multilayer network analysis of nuclear reactions
• Bias-Variance Tradeoffs in Joint Spectral Embeddings
• Collaborative similarity analysis of multilayer developer-project bipartite network
• Multiscale modeling of brain network organization
• Patterns of Multiplex Layer Entanglement across Real and Synthetic Networks
• Community detection over a heterogeneous population of non-aligned networks
• Graphlets in multilayer networks
• Discriminative community detection for multiplex networks