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In this paper we compare the combinatorial Ricci curvature on cell complexesand the LLY-Ricci curvature defined on graphs. A cell complex is correspondenceto a graph such that the vertexes are cells and the edges are vectors on thecell complex. We compare this two Ricci curvature by the cooupling andKantrovich duality.

Relation between combinatorial Ricci curvature and Lin-Lu-Yau's Ricci Curvature on cell complexes