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Title: Curvature on graphs via equilibrium measures
Abstract We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by have diameter bounded by (a Bonnet–Myers theorem), that implies that has constant curvature (a Cheng theorem) and that there is a spectral gap (a Lichnerowicz theorem). It is computed for several families of graphs and often coincides with Ollivier curvature or Lin–Lu–Yau curvature. The von Neumann Minimax theorem features prominently in the proofs.  more » « less
Award ID(s):
2123224
PAR ID:
10419864
Author(s) / Creator(s):
 
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Journal of Graph Theory
Volume:
103
Issue:
3
ISSN:
0364-9024
Page Range / eLocation ID:
p. 415-436
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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