Twisted edge Laplacians on finite graphs from a K\'{a}hler structure

In this paper we study a Kahler structure on finite points. In particular, we study the edge Laplacian of a graph twisted by the Kahler structure introduced in this paper. We also discuss a metric aspect from a twisted holomorphic Dolbeault-Dirac spectral triple and show that the points have a finite diameter with respect to Connes' distance.
Comment: 14 pages