Nonnegative Bakry--Émery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincaré Inequalities

Qi Guo, Xueping Huang, Yi C. Huang

We prove that every connected simple graph of bounded degree satisfying the classical dimension-free Bakry--Émery condition $\mathrm{CD}(0,\infty )$ for the unnormalised Laplacian i…