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

Relation between Combinatorial Ricci Curvature and Lin-Lu-Yau's Ricci Curvature on Cell Complexes