  We study a nonlinear wave equation on finite connected weighted graphs. Using
Rothe's and energy methods, we prove the existence and uniqueness of solution
under certain assumption. For linear wave equation on graphs, Lin and Xie
\cite{Lin-Xie} obtained the existence and uniqueness of solution. The main
novelty of this paper is that the wave equation we considered has the nonlinear
damping term $|u_t|^{p-1}\cdot u_t$ ($p>1$).
