# Multilayer Networks

arXiv: https://arxiv.org/abs/1309.7233 · HTML: https://mlsanity.com/paper/1309.7233/

## Key facts

- Cited by 87 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2013.

## Built on by (most cited first, 30 of 87)

- [Compound Word Transformer: Learning to Compose Full-Song Music over Dynamic Directed Hypergraphs](https://mlsanity.com/paper/2101.02402/) (2021)
- [A Comprehensive Survey on Community Detection with Deep Learning](https://mlsanity.com/paper/2105.12584/) (2021)
- [On the Impact of Overparameterization on the Training of a Shallow Neural Network in High Dimensions](https://mlsanity.com/paper/2311.03794/) (2023)
- [A Survey on Data-driven Software Vulnerability Assessment and Prioritization](https://mlsanity.com/paper/2107.08364/) (2021)
- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Scholastic: Graphical Human-Al Collaboration for Inductive and Interpretive Text Analysis](https://mlsanity.com/paper/2208.06133/) (2022)
- [ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network](https://mlsanity.com/paper/2102.10226/) (2021)
- [Time Series Analysis via Network Science: Concepts and Algorithms](https://mlsanity.com/paper/2110.09887/) (2021)
- [Semi-Supervised Deep Learning for Multiplex Networks](https://mlsanity.com/paper/2110.02038/) (2021)
- [Fusing Modalities by Multiplexed Graph Neural Networks for Outcome Prediction in Tuberculosis](https://mlsanity.com/paper/2210.14377/) (2022)
- [Anomaly Detection in Multiplex Dynamic Networks: from Blockchain Security to Brain Disease Prediction](https://mlsanity.com/paper/2211.08378/) (2022)
- [Conjugate Product Graphs for Globally Optimal 2D-3D Shape Matching](https://mlsanity.com/paper/2211.11589/) (2022)
- [Supra-Laplacian Encoding for Transformer on Dynamic Graphs](https://mlsanity.com/paper/2409.17986/) (2024)
- [Ranking with multiple types of pairwise comparisons](https://mlsanity.com/paper/2206.13580/) (2022)
- [CS-MLGCN : Multiplex Graph Convolutional Networks for Community Search in Multiplex Networks](https://mlsanity.com/paper/2210.08811/) (2022)
- [Attention-based Dynamic Multilayer Graph Neural Networks for Loan Default Prediction](https://mlsanity.com/paper/2402.00299/) (2024)
- [Nonparametric Modeling of Higher-Order Interactions via Hypergraphons](https://mlsanity.com/paper/2105.08678/) (2021)
- [mGNN: Generalizing the Graph Neural Networks to the Multilayer Case](https://mlsanity.com/paper/2109.10119/) (2021)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network](https://mlsanity.com/paper/2208.13179/) (2022)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Multilayer Networks for Text Analysis with Multiple Data Types](https://mlsanity.com/paper/2106.15821/) (2021)
- [Hypergraphon Mean Field Games](https://mlsanity.com/paper/2203.16223/) (2022)
- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Universal Multilayer Network Exploration by Random Walk with Restart](https://mlsanity.com/paper/2107.04565/) (2021)
- [SciNoBo : A Hierarchical Multi-Label Classifier of Scientific Publications](https://mlsanity.com/paper/2204.00880/) (2022)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Multilayer hypergraph clustering using the aggregate similarity matrix](https://mlsanity.com/paper/2301.11657/) (2023)

## 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.