# Layer aggregation and reducibility of multilayer interconnected networks

arXiv: https://arxiv.org/abs/1405.0425 · HTML: https://mlsanity.com/paper/1405.0425/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2014.

## Built on by (most cited first, 30 of 34)

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- [Optimal Estimation and Computational Limit of Low-rank Gaussian Mixtures](https://mlsanity.com/paper/2201.09040/) (2022)
- [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)
- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks](https://mlsanity.com/paper/2111.15018/) (2021)
- [Hierarchical Aggregations for High-Dimensional Multiplex Graph Embedding](https://mlsanity.com/paper/2312.16834/) (2023)
- [Learning Joint and Individual Structure in Network Data with Covariates](https://mlsanity.com/paper/2406.08776/) (2024)
- [A Geometric Perspective for High-Dimensional Multiplex Graphs](https://mlsanity.com/paper/2501.17374/) (2025)
- [Hypergraph Dissimilarity Measures](https://mlsanity.com/paper/2106.08206/) (2021)
- [Systematic assessment of the quality of fit of the stochastic block model for empirical networks](https://mlsanity.com/paper/2201.01658/) (2022)
- [rMultiNet: An R Package For Multilayer Networks Analysis](https://mlsanity.com/paper/2302.04437/) (2023)
- [Signed Diverse Multiplex Networks: Clustering and Inference](https://mlsanity.com/paper/2402.10242/) (2024)
- [MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization](https://mlsanity.com/paper/2402.16898/) (2024)
- [The role of System 1 and System 2 semantic memory structure in human and LLM biases](https://mlsanity.com/paper/2604.12816/) (2026)
- [On consistency of constrained spectral clustering under representation-aware stochastic block model](https://mlsanity.com/paper/2203.02005/) (2022)
- [MultiSAGE: a multiplex embedding algorithm for inter-layer link prediction](https://mlsanity.com/paper/2206.13223/) (2022)
- [Cognitive modelling with multilayer networks: Insights, advancements and future challenges](https://mlsanity.com/paper/2210.00500/) (2022)
- [Random Walk on Multiple Networks](https://mlsanity.com/paper/2307.01637/) (2023)
- [Mixture of multilayer stochastic block models for multiview clustering](https://mlsanity.com/paper/2401.04682/) (2024)
- [MPXGAT: An Attention based Deep Learning Model for Multiplex Graphs Embedding](https://mlsanity.com/paper/2403.19246/) (2024)
- [Estimating mixed memberships in multi-layer networks](https://mlsanity.com/paper/2404.03916/) (2024)
- [Beyond holography: the entropic quantum gravity foundations of image processing](https://mlsanity.com/paper/2503.14048/) (2025)
- [Transfer learning under latent space model](https://mlsanity.com/paper/2509.15797/) (2025)

## Abstract (arXiv)

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, with thousands of protein-protein interactions each. A fundamental open question is then how much information is really necessary to accurately represent the structure of a multilayer complex system, and if and when some of the layers can indeed be aggregated. Here we introduce a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss. We validate our approach on a set of synthetic benchmarks, and prove its applicability to an extended data set of protein-genetic interactions, showing cases where a strong reduction is possible and cases where it is not. Using this method we can describe complex systems with an optimal trade--off between accuracy and complexity.