Multilayer stochastic block models reveal the multilayer structure of complex networks

Abstract

In complex systems, the network of interactions we observe between system's components is the aggregate of the interactions that occur through different mechanisms or layers. Recent studies reveal that the existence of multiple interaction layers can have a dramatic impact in the dynamical processes occurring on these systems. However, these studies assume that the interactions between systems components in each one of the layers are known, while typically for real-world systems we do not have that information. Here, we address the issue of uncovering the different interaction layers from aggregate data by introducing multilayer stochastic block models (SBMs), a generalization of single-layer SBMs that considers different mechanisms of layer aggregation. First, we find the complete probabilistic solution to the problem of finding the optimal multilayer SBM for a given aggregate observed network. Because this solution is computationally intractable, we propose an approximation that enables us to verify that multilayer SBMs are more predictive of network structure in real-world complex systems.

References in corpus (16)

• Hierarchical structure and the prediction of missing links in networks
• Stochastic blockmodels and community structure in networks
• Community Structure in Jazz
• Diffusion dynamics on multiplex networks
• Missing and spurious interactions and the reconstruction of complex networks
• Extracting the hierarchical organization of complex systems
• Classes of complex networks defined by role-to-role connectivity profiles
• Phase transition in the detection of modules in sparse networks
• Transport on coupled spatial networks
• Parsimonious module inference in large networks
• Learning Latent Block Structure in Weighted Networks
• Efficiently inferring community structure in bipartite networks
• A network inference method for large-scale unsupervised identification of novel drug-drug interactions
• Justice blocks and predictability of US Supreme Court votes
• Predicting human preferences using the block structure of complex social networks
• Predicting future conflict between team-members with parameter-free models of social networks

Cited by in corpus (20)

• Community detection, link prediction, and layer interdependence in multilayer networks
• Master stability functions for complete, intra-layer and inter-layer synchronization in multiplex networks
• Bayesian stochastic blockmodeling
• Detectability thresholds and optimal algorithms for community structure in dynamic networks
• Clustering Network Layers With the Strata Multilayer Stochastic Block Model
• Enhanced detectability of community structure in multilayer networks through layer aggregation
• Multilink Communities of Multiplex Networks
• Consistencies and inconsistencies between model selection and link prediction in networks
• A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks
• Network structure, metadata and the prediction of missing nodes and annotations
• Classifying Patents Based on their Semantic Content
• Multilayer Network Science: from Cells to Societies
• Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem
• A Unified Method of Detecting Core-Periphery Structure and Community Structure in Networks
• Community Detection and Improved Detectability in Multiplex Networks
• Identifying multi-scale communities in networks by asymptotic surprise
• Atomic subgraphs and the statistical mechanics of networks
• Inference of Edge Correlations in Multilayer Networks
• A useful criterion on studying consistent estimation in community detection
• Multiplex reconstruction with partial information