This paper defines a positive semidefinite operator called \(\epsilon -\) repelling Laplacian on any positive connected signed graph. \(\epsilon \) is an arbitrary positive number less than a constant \(\epsilon _0\) related to the graph’s consensus problem. Then we use the pseudoinverse of \(\epsilon -\) repelling Laplacian to construct \(\epsilon -\) repelling cost as an analogue of graph’s effective resistance. Subsequently, we define some novel discrete curvatures on any positive connected signed graph called node and edge \(\epsilon -\) repelling curvature, as a generalization of resistance curvatures proposed by K. Devriendt et al.. Besides, we derive the corresponding Lichnerowicz inequalities. Moreover, it turns out that edge \(\epsilon -\) repelling curvature is no more than the Lin-Lu-Yau curvature based on \(\epsilon -\) repelling cost of the underlying graph.
