2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70974It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rank-connectivity. In terms of statistical physics, this can be viewed as a characterization of partition functions of vertex models.17 pages LatexCombinatoricsMathematical Physics05C99 (Primary), 82B99 (Secondary)text