Condensed Ricci curvature of complete and strongly regular graphs

  title={Condensed Ricci curvature of complete and strongly regular graphs},
  author={Vincent Bonini and Conor Carroll and Uyen N. Dinh and Sydney Dye and Joshua Frederick and Erin P. J. Pearse},
  journal={arXiv: Combinatorics},
We study a modified notion of Ollivier's coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for complete graphs that shows a connected finite simple graph is complete if and only if the Ricci curvature is strictly greater than one. We then derive explicit Ricci curvature formulas for strongly regular graphs in terms of the graph parameters and the size of a maximal matching in the core neighborhood. As a consequence we are able to derive… 

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