摘要：We introduce the nonlinear Schr\"{o}dinger equation on a locally finite graph. Via the Nehari method, if $a(x)$ satisfies certain assumptions, for any $\lambda>0$, we show that the equation admits a positive ground state solution. Moreover, for $\lambda\rightarrow \infty$, the solution $u_\lambda$ converges to a solution of the limit Dirichlet problem which is defined on the potential well. We also provide a numerical result for an example to illustrate our results.