# Community detection, link prediction, and layer interdependence in multilayer networks

arXiv: https://arxiv.org/abs/1701.01369 · HTML: https://mlsanity.com/paper/1701.01369/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2017.

## Built on by (most cited first, 17 of 17)

- [Inference of hyperedges and overlapping communities in hypergraphs](https://mlsanity.com/paper/2204.05646/) (2022)
- [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023)
- [Estimating Social Influence from Observational Data](https://mlsanity.com/paper/2204.01633/) (2022)
- [Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks](https://mlsanity.com/paper/2505.21748/) (2025)
- [The interplay between ranking and communities in networks](https://mlsanity.com/paper/2112.12670/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Flexible inference in heterogeneous and attributed multilayer networks](https://mlsanity.com/paper/2405.20918/) (2024)
- [A graph representation based on fluid diffusion model for data analysis: theoretical aspects and enhanced community detection](https://mlsanity.com/paper/2112.04388/) (2021)
- [Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models](https://mlsanity.com/paper/2401.00688/) (2024)
- [Community Detection in the Multi-View Stochastic Block Model](https://mlsanity.com/paper/2401.09510/) (2024)
- [The ALℓ0CORE Tensor Decomposition for Sparse Count Data](https://mlsanity.com/paper/2403.06153/) (2024)
- [Multilayer Correlation Clustering](https://mlsanity.com/paper/2404.16676/) (2024)
- [Multi-View Stochastic Block Models](https://mlsanity.com/paper/2406.04860/) (2024)
- [Hierarchical Blockmodelling for Knowledge Graphs](https://mlsanity.com/paper/2408.15649/) (2024)
- [How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?](https://mlsanity.com/paper/2506.11869/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)
- [Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection](https://mlsanity.com/paper/2610.01361/) (2026)

## Abstract (arXiv)

Complex systems are often characterized by distinct types of interactions between the same entities. These can be described as a multilayer network where each layer represents one type of interaction. These layers may be interdependent in complicated ways, revealing different kinds of structure in the network. In this work we present a generative model, and an efficient expectation-maximization algorithm, which allows us to perform inference tasks such as community detection and link prediction in this setting. Our model assumes overlapping communities that are common between the layers, while allowing these communities to affect each layer in a different way, including arbitrary mixtures of assortative, disassortative, or directed structure. It also gives us a mathematically principled way to define the interdependence between layers, by measuring how much information about one layer helps us predict links in another layer. In particular, this allows us to bundle layers together to compress redundant information, and identify small groups of layers which suffice to predict the remaining layers accurately. We illustrate these findings by analyzing synthetic data and two real multilayer networks, one representing social support relationships among villagers in South India and the other representing shared genetic substrings material between genes of the malaria parasite.