In this note, we provide Steinerberger curvature formulas for block graphs, discuss curvature relations between two graphs and the graph obtained by connecting them via a bridge, and show that self-centered Bonnet-Myers sharp graphs are precisely those which are antipodal. We also discuss similarities and differences between Steinerberger and Ollivier Ricci curvature results.
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Cushing et al. (2024) studied this question.
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