{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/accurately-modeling-biased-random-walks-on","title":"Accurately Modeling Biased Random Walks on Weighted Graphs Using $\\textit{Node2vec+}$","arxiv_id":"2109.08031","date":"2021-09-15","proceeding":null,"authors":["Renming Liu","Matthew Hirn","Arjun Krishnan"],"abstract":"Node embedding is a powerful approach for representing the structural role of each node in a graph. $\\textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. However, $\\textit{node2vec}$ does not consider edge weights when computing walk biases. This intrinsic limitation prevents $\\textit{node2vec}$ 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 $\\textit{node2vec}$ to $\\textit{node2vec+}$ in a way that accounts for edge weights when calculating walk biases, but which reduces to $\\textit{node2vec}$ in the cases of unweighted graphs or unbiased walks. We empirically show that $\\textit{node2vec+}$ is more robust to additive noise than $\\textit{node2vec}$ in weighted graphs using two synthetic datasets. We also demonstrate that $\\textit{node2vec+}$ significantly outperforms $\\textit{node2vec}$ on a commonly benchmarked multi-label dataset (Wikipedia). Furthermore, we test $\\textit{node2vec+}$ 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 $\\textit{node2vec+}$. Finally, $\\textit{node2vec+}$ can be used as a general approach for generating biased random walks, benefiting all existing methods built on top of $\\textit{node2vec}$. $\\textit{Node2vec+}$ is implemented as part of $\\texttt{PecanPy}$, which is available at https://github.com/krishnanlab/PecanPy .","url_abs":"https://arxiv.org/abs/2109.08031v2","url_pdf":"https://arxiv.org/pdf/2109.08031v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"accurately-modeling-biased-random-walks-on","repo_url":"https://github.com/krishnanlab/PecanPy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"gcn","method_name":"GCN"},{"method_slug":"graphsage","method_name":"GraphSAGE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}