Garcia-Pulido, Ana LuciaHess, KathrynTan, JaneTurner, KatharineWang, BeiYerolemou, Naya2025-03-152025-03-152364-5733researchoutputwizard:a383154xPUB34274Scopus:85130549408https://dspace-test.anu.edu.au/handle/1885/733716694We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has often been observed that phenomena exhibited by real-world networks reflect the topology of their flag complexes, as measured, for example, by Betti numbers or simplex counts. As it is often computationally expensive (or even unfeasible) to determine such topological features exactly, it would be extremely valuable to have pseudometrics on the set of directed graphs that can both detect the topological differences and be computed efficiently. To facilitate work in this direction, we introduce methods to measure how well a graph pseudometric captures the topology of a directed graph. We then use these methods to evaluate some well-established pseudometrics, using test data drawn from several families of random graphs.Acknowledgments This work began at the Women in Computational Topology Workshop in 2019. The authors wish to thank the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute, and the Association of Women in Mathematics for their financial support. ALGP is supported by the EPSRC grant “New Approaches to Data Science: Application Driven Topological Data Analysis” EP/R018472/1. NY is supported by the Alan Turing Institute under the EPSRC grant EP/N510129/1. KT is supported by an ARC DECRA fellowship. BW is supported in part by DOE DE-SC0021015 and NSF DBI-1661375. The authors would also like to thank Erika Roldán for insightful contributions, Gesine Reinert for sharing the source code for TriadEMD and TriadEuclid, the Oxford Mathematical Institute for providing access to computational resources, and the anonymous referees whose comments have helped to clarify this paper.30EnglishPublisher Copyright: © 2022, The Author(s) and the Association for Women in Mathematics.202210.1007/978-3-030-95519-9_5http://www.scopus.com/inward/record.url?scp=85130549408&partnerID=8YFLogxK