# Random Walk on Multiple Networks

arXiv: https://arxiv.org/abs/2307.01637 · HTML: https://mlsanity.com/paper/2307.01637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 63 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Graph Meta Network for Multi-Behavior Recommendation](https://mlsanity.com/paper/2110.03969/) (2021)
- [Layer aggregation and reducibility of multilayer interconnected networks](https://mlsanity.com/paper/1405.0425/) (2014)
- [Heat kernel based community detection](https://mlsanity.com/paper/1403.3148/) (2014)
- [Multiplex Heterogeneous Graph Convolutional Network](https://mlsanity.com/paper/2208.06129/) (2022)
- [Uncovering the Small Community Structure in Large Networks: A Local Spectral Approach](https://mlsanity.com/paper/1509.07715/) (2015)
- [Flow-Based Local Graph Clustering with Better Seed Set Inclusion](https://mlsanity.com/paper/1811.12280/) (2018)
- [Characterizing interactions in online social networks during exceptional events](https://mlsanity.com/paper/1506.09115/) (2015)
- [Bibliographic Analysis on Research Publications using Authors, Categorical Labels and the Citation Network](https://mlsanity.com/paper/1609.06532/) (2016)

## Abstract (arXiv)

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited information. In contrast, real data often contain entities with different types or/and from different sources, which are comprehensive and can be better modeled by multiple networks. To take advantage of rich information in multiple networks and make better inferences on entities, in this study, we propose random walk on multiple networks, RWM. RWM is flexible and supports both multiplex networks and general multiple networks, which may form many-to-many node mappings between networks. RWM sends a random walker on each network to obtain the local proximity (i.e., node visiting probabilities) w.r.t. the starting nodes. Walkers with similar visiting probabilities reinforce each other. We theoretically analyze the convergence properties of RWM. Two approximation methods with theoretical performance guarantees are proposed for efficient computation. We apply RWM in link prediction, network embedding, and local community detection. Comprehensive experiments conducted on both synthetic and real-world datasets demonstrate the effectiveness and efficiency of RWM.