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

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Abstract

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

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Sep 17

Keywords

  • Comparison geometry
  • Directed graph
  • Eigenvalue of Laplacian
  • Ricci curvature

ASJC Scopus subject areas

  • General

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