# Universal Multilayer Network Exploration by Random Walk with Restart

arXiv: https://arxiv.org/abs/2107.04565 · HTML: https://mlsanity.com/paper/2107.04565/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 55 references that are in the map.
- First posted on arXiv 9 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [The structure and dynamics of multilayer networks](https://mlsanity.com/paper/1407.0742/) (2014)
- [Random Walks on Multiplex Networks](https://mlsanity.com/paper/1306.0519/) (2013)
- [MultiVERSE: a multiplex and multiplex-heterogeneous network embedding approach](https://mlsanity.com/paper/2008.10085/) (2020)
- [GrAMME: Semi-Supervised Learning using Multi-layered Graph Attention Models](https://mlsanity.com/paper/1810.01405/) (2018)
- [MGCN: Semi-supervised Classification in Multi-layer Graphs with Graph Convolutional Networks](https://mlsanity.com/paper/1811.08800/) (2018)
- [Recent Advances in Network-based Methods for Disease Gene Prediction](https://mlsanity.com/paper/2007.10848/) (2020)
- [Structural measures for multiplex networks](https://mlsanity.com/paper/1308.3182/) (2013)

## Built on by (most cited first, 2 of 2)

- [MSGCN: Multiplex Spatial Graph Convolution Network for Interlayer Link Weight Prediction](https://mlsanity.com/paper/2504.17749/) (2025)
- [Embedding Learning on Multiplex Networks for Link Prediction](https://mlsanity.com/paper/2602.01922/) (2026)

## Abstract (arXiv)

The amount and variety of data is increasing drastically for several years. These data are often represented as networks, which are then explored with approaches arising from network theory. Recent years have witnessed the extension of network exploration methods to leverage more complex and richer network frameworks. Random walks, for instance, have been extended to explore multilayer networks. However, current random walk approaches are limited in the combination and heterogeneity of network layers they can handle. New analytical and numerical random walk methods are needed to cope with the increasing diversity and complexity of multilayer networks. We propose here MultiXrank, a Python package that enables Random Walk with Restart (RWR) on any kind of multilayer network with an optimized implementation. This package is supported by a universal mathematical formulation of the RWR. We evaluated MultiXrank with leave-one-out cross-validation and link prediction, and introduced protocols to measure the impact of the addition or removal of multilayer network data on prediction performances. We further measured the sensitivity of MultiXrank to input parameters by in-depth exploration of the parameter space. Finally, we illustrate the versatility of MultiXrank with different use-cases of unsupervised node prioritization and supervised classification in the context of human genetic diseases.