# Multilayer stochastic block models reveal the multilayer structure of complex networks

arXiv: https://arxiv.org/abs/1411.1098 · HTML: https://mlsanity.com/paper/1411.1098/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2014.

## Built on by (most cited first, 7 of 7)

- [Multilayer Networks for Text Analysis with Multiple Data Types](https://mlsanity.com/paper/2106.15821/) (2021)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Community Detection in Weighted Multilayer Networks with Ambient Noise](https://mlsanity.com/paper/2103.00486/) (2021)
- [A Simple Quantum Blockmodeling with Qubits and Permutations](https://mlsanity.com/paper/2311.07726/) (2023)
- [VEC-SBM: Optimal Community Detection with Vectorial Edges Covariates](https://mlsanity.com/paper/2402.18805/) (2024)
- [Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals](https://mlsanity.com/paper/2509.15989/) (2025)
- [Learning Multi-Order Block Structure in Higher-Order Networks](https://mlsanity.com/paper/2511.21350/) (2025)

## Abstract (arXiv)

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.