Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

Understand

For undirected graphs, the Ricci curvature introduced by Lin-Lu-Yau has been widely studied from various perspectives, especially geometric analysis.

• In the present paper, we discuss generalization problem of their Ricci curvature for directed graphs.
• We introduce a new generalization by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian.
• We conclude several geometric and spectral properties of directed graphs under a lower Ricci curvature bound extending previous results in the undirected case.