# Accurately Modeling Biased Random Walks on Weighted Graphs Using textitNode2vec+

arXiv: https://arxiv.org/abs/2109.08031 · HTML: https://mlsanity.com/paper/2109.08031/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluations](https://mlsanity.com/paper/1906.05017/) (2019)
- [word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings of Structured Data](https://mlsanity.com/paper/2003.12590/) (2020)
- [k-simplex2vec: a simplicial extension of node2vec](https://mlsanity.com/paper/2010.05636/) (2020)
- [Asymptotics of Network Embeddings Learned via Subsampling](https://mlsanity.com/paper/2107.02363/) (2021)
- [Het-node2vec: second order random walk sampling for heterogeneous multigraphs embedding](https://mlsanity.com/paper/2101.01425/) (2021)
- [Community Structure aware Embedding of Nodes in a Network](https://mlsanity.com/paper/2006.15313/) (2020)

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

- [Designing weighted and multiplex networks for deep learning user geolocation in Twitter](https://mlsanity.com/paper/2112.06999/) (2021)
- [Edge Ranking of Graphs in Transportation Networks using a Graph Neural Network (GNN)](https://mlsanity.com/paper/2303.17485/) (2023)

## Abstract (arXiv)

Node embedding is a powerful approach for representing the structural role of each node in a graph. textitNode2vec is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. However, textitnode2vec does not consider edge weights when computing walk biases. This intrinsic limitation prevents textitnode2vec from leveraging all the information in weighted graphs and, in turn, limits its application to many real-world networks that are weighted and dense. Here, we naturally extend textitnode2vec to textitnode2vec+ in a way that accounts for edge weights when calculating walk biases, but which reduces to textitnode2vec in the cases of unweighted graphs or unbiased walks. We empirically show that textitnode2vec+ is more robust to additive noise than textitnode2vec in weighted graphs using two synthetic datasets. We also demonstrate that textitnode2vec+ significantly outperforms textitnode2vec on a commonly benchmarked multi-label dataset (Wikipedia). Furthermore, we test textitnode2vec+ against GCN and GraphSAGE using various challenging gene classification tasks on two protein-protein interaction networks. Despite some clear advantages of GCN and GraphSAGE, they show comparable performance with textitnode2vec+. Finally, textitnode2vec+ can be used as a general approach for generating biased random walks, benefiting all existing methods built on top of textitnode2vec. textitNode2vec+ is implemented as part of textttPecanPy, which is available at https://github.com/krishnanlab/PecanPy .