TY - JOUR
T1 - Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
AU - Ozawa, Ryunosuke
AU - Sakurai, Yohei
AU - Yamada, Taiki
N1 - Funding Information:
The authors are grateful to the anonymous referees for valuable comments. The first author was supported in part by JSPS KAKENHI (19K14532). The first and second authors were supported in part by JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design” (17H06460).
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - 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 for strongly connected directed graphs by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian. We conclude several geometric and spectral properties under a lower Ricci curvature bound extending previous results in the undirected case.
AB - 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 for strongly connected directed graphs by using the mean transition probability kernel which appears in the formulation of the Chung Laplacian. We conclude several geometric and spectral properties under a lower Ricci curvature bound extending previous results in the undirected case.
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U2 - 10.1007/s00526-020-01809-2
DO - 10.1007/s00526-020-01809-2
M3 - Article
AN - SCOPUS:85089496320
VL - 59
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 4
M1 - 142
ER -