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.
MSC Codes 05C20, 05C12, 05C81, 53C21, 53C23
|Publication status||Published - 2019 Sep 17|
- Comparison geometry
- Directed graph
- Eigenvalue of Laplacian
- Ricci curvature
ASJC Scopus subject areas