On the Diffusion Geometry of Graph Laplacians and Applications

Xiuyuan Cheng, Manas Rachh, Stefan Steinerberger

We study directed, weighted graphs $G=(V,E)$ and consider the (not necessarily symmetric) averaging operator $$(\mathcal{L}u)(i)=-\sum _{j{\sim }_{}i}{p}_{ij}(u(j)-u(i)),$$ whe…