The article discusses the importance of comparing graphs using optimal transport distances, focusing on directed graphs. It introduces two distance measures, including an Earth Movers Distance (Wasserstein) and a Gromov-Wasserstein (GW) distance, to compare directed graphs. The study evaluates these distances using simulated graph data and real-world cell-cell communication networks derived from single-cell RNA-seq data. Most optimal transport methods have been developed for undirected graphs, but this study addresses the challenges of extending these methods to directed graphs. By considering node-to-node distances like Generalized Effective Resistance (GRD) and Markov chain hitting time (HTD), the authors propose ways to compute optimal transport-based graph distances for directed graphs. These metrics are evaluated in clustering cell-cell communication networks from single-cell sequencing data, which present challenges due to technical artifacts like missing connections and noise.
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by James S. Nag... alle arxiv.org 03-15-2024
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