9) "A global Poincare inequality on graphs via a conical curvature­ dimension conditions", joint with Z. McGuirk, Analysis and Geometry in Metric Spaces (2018)

We introduce and study the conical curvature-dimension condition, CCD(K, N), for finite graphs. We show that CCD(K, N) provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs. Another application of the conical curvature-dimension analysis is finding a sharp estimate on the curvature of complete graphs.