  We study nonexistence and existence of nontrivial positive solutions to the
following semilinear elliptic inequality involving gradient terms
  \[
  \Delta u+u^p\left|\nabla u\right|^q\leq0,
  \] on weighted graphs, where $(p,q)\in\mathbb{R}^2$. We give a complete
classification of $(p,q)$ under which sharp volume growth assumptions are
established.
