Optimal transport distances for directed, weighted graphs: a case study with cell-cell communication networks
This work addresses the challenge of quantifying differences in directed graphs, which is incremental as it extends existing optimal transport methods from undirected to directed graphs.
The authors tackled the problem of comparing directed graphs by proposing two optimal transport-based distance measures, an earth mover's distance and a Gromov-Wasserstein distance, and evaluated their performance on simulated and real-world cell-cell communication networks.
Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the associated changes between graphs in terms of a transport plan. As the lack of symmetry introduces challenges in the typically considered formulations, optimal transport distances for graphs have mostly been developed for undirected graphs. Here, we propose two distance measures to compare directed graphs based on variants of optimal transport: (i) an earth movers distance (Wasserstein) and (ii) a Gromov-Wasserstein (GW) distance. We evaluate these two distances and discuss their relative performance for both simulated graph data and real-world directed cell-cell communication graphs, inferred from single-cell RNA-seq data.