Ollivier–Ricci idleness functions of graphs

David P. Bourne, D. Cushing, S. Liu, F. Münch, N. Peyerimhoff

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)
69 Downloads (Pure)


We study the Ollivier–Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.

Original languageEnglish
Pages (from-to)1408-1424
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number2
Publication statusPublished - 19 Jun 2018


  • Idleness
  • Ollivier–Ricci
  • Optimal transport

ASJC Scopus subject areas

  • General Mathematics


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