mlsanityData to 7 Oct 2026

Multilayer Networks

arXiv 1309.7233 ↗First posted 27 Sep 2013physics.soc-ph cs.SIcited by 86

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Abstract (arXiv)

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.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Sep 2013.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 19; 2022: 17; 2023: 12; 2024: 12; 2025: 12; 2026: 14.

86 papers.

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  1. 2021Compound Word Transformer: Learning to Compose Full-Song Music over Dynamic Directed Hypergraphscited by 109
  2. 2021A Comprehensive Survey on Community Detection with Deep Learningcited by 63
  3. 2023On the Impact of Overparameterization on the Training of a Shallow Neural Network in High Dimensionscited by 21
  4. 2021A Survey on Data-driven Software Vulnerability Assessment and Prioritizationcited by 18
  5. 2021Machine learning dismantling and early-warning signals of disintegration in complex systemscited by 14
  6. 2021Latent Space Model for Higher-order Networks and Generalized Tensor Decompositioncited by 13
  7. 2022Scholastic: Graphical Human-Al Collaboration for Inductive and Interpretive Text Analysiscited by 12
  8. 2021ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Networkcited by 8
  9. 2021Time Series Analysis via Network Science: Concepts and Algorithmscited by 8
  10. 2021Semi-Supervised Deep Learning for Multiplex Networkscited by 6
  11. 2022Fusing Modalities by Multiplexed Graph Neural Networks for Outcome Prediction in Tuberculosiscited by 6
  12. 2022Anomaly Detection in Multiplex Dynamic Networks: from Blockchain Security to Brain Disease Predictioncited by 6
38 more
  1. 2022Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matchingcited by 6
  2. 2024Supra-Laplacian Encoding for Transformer on Dynamic Graphscited by 6
  3. 2022CS-MLGCN : Multiplex Graph Convolutional Networks for Community Search in Multiplex Networkscited by 5
  4. 2024Attention-based Dynamic Multilayer Graph Neural Networks for Loan Default Predictioncited by 5
  5. 2021Nonparametric Modeling of Higher-Order Interactions via Hypergraphonscited by 4
  6. 2021mGNN: Generalizing the Graph Neural Networks to the Multilayer Casecited by 4
  7. 2022Sparse Subspace Clustering in Diverse Multiplex Network Modelcited by 4
  8. 2022Ranking with multiple types of pairwise comparisonscited by 4
  9. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  10. 2021Multilayer Networks for Text Analysis with Multiple Data Typescited by 3
  11. 2022Hypergraphon Mean Field Gamescited by 3
  12. 2022Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Networkcited by 3
  13. 2024Community detection by spectral methods in multi-layer networkscited by 3
  14. 2021Clustering multilayer graphs with missing nodescited by 2
  15. 2021Universal Multilayer Network Exploration by Random Walk with Restartcited by 2
  16. 2022SciNoBo : A Hierarchical Multi-Label Classifier of Scientific Publicationscited by 2
  17. 2022Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorizationcited by 2
  18. 2023Multilayer hypergraph clustering using the aggregate similarity matrixcited by 2
  19. 2023Zoo Guide to Network Embeddingcited by 2
  20. 2023Privacy-Preserving Community Detection for Locally Distributed Multiple Networkscited by 2
  21. 2023Hierarchical Aggregations for High-Dimensional Multiplex Graph Embeddingcited by 2
  22. 2025A Geometric Perspective for High-Dimensional Multiplex Graphscited by 2
  23. 2025Identifying Super Spreaders in Multilayer Networkscited by 2
  24. 2026Emergence of Fragility in LLM-based Social Networks: the Case of Moltbookcited by 2
  25. 2021Designing weighted and multiplex networks for deep learning user geolocation in Twittercited by 1
  26. 2022Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCAcited by 1
  27. 2022From Time Series to Networks in R with the ts2net Packagecited by 1
  28. 2022Efficient multi-relational network representation using primescited by 1
  29. 2023A Network Science perspective of Graph Convolutional Networks: A surveycited by 1
  30. 2024Community Detection in the Multi-View Stochastic Block Modelcited by 1
  31. 2024Signed Diverse Multiplex Networks: Clustering and Inferencecited by 1
  32. 2024Tensor Methods in High Dimensional Data Analysis: Opportunities and Challengescited by 1
  33. 2025Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Networkcited by 1
  34. 2025Multilayer Artificial Benchmark for Community Detection (mABCD)cited by 1
  35. 2025Fuzzy Hierarchical Multiplexcited by 1
  36. 2026STAR-Teaming: A Strategy-Response Multiplex Network Approach to Automated LLM Red Teamingcited by 1
  37. 2021A Tensor-Based Formulation of Hetero-functional Graph Theorycited by 0
  38. 2021Overcoming Bias in Community Detection Evaluationcited by 0

50 most cited of 86 All 86 (JSON)