2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155526The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semigroups on metric graphs.Functional AnalysisMathematical Physics34B45, 47D06, 47B44text