I'm reading a paper.It says
if $M$ is a projective algebraic variety and $f:N-S\rightarrow M$ is a holomorphic map,where $N$ is a connected complex manifold and $S\subset N$ is a proper analytic subset.Then the closure $\overline{\Gamma_f}\subset N\times M$ of the graph $\Gamma_f=\{(x,f(x)):x\in N-S\}\subset (N-S)\times M$ is an analytic subset of $N\times M$ iff the pullbacks $f^\ast\varphi$ of all rational functions on $M$ extend to a meromorphic functions on $N$.
I don't know how to prove this proposition.Can you help me?Thanks in advance!