First Betti number of the path homology of random directed graphs
Posted to site: 17/05/22
Path homology is a topological invariant for directed graphs, which is sensitive to their asymmetry and can discern between digraphs which are indistinguishable to the directed flag complex. In Erdös-Rényi directed random graphs, the first Betti number undergoes two distinct transitions, appearing at a low-density boundary and vanishing again at a high-density boundary. In this video, I briefly describe techniques for studying these transitions, with more details on the arXiv pre-print.
This work was completed whilst I was a member of the Centre for Topological Data Analysis, which is funded by the EPSRC grant ‘New Approaches to Data Science: Application Driven Topological Data Analysis’ EP/R018472/1.