  Let $S$ be a closed, connected, orientable surface of genus at least 3,
$\mathcal{C}(S)$ be the complex of curves on $S$ and $Mod_S^*$ be the extended
mapping class group of $S$. We prove that a simplicial map, $\lambda:
\mathcal{C}(S) \to \mathcal{C}(S)$, preserves nondisjointness (i.e. if $\alpha$
and $\beta$ are two vertices in $\mathcal{C}(S)$ and $i(\alpha, \beta) \neq 0$,
then $i(\lambda(\alpha), \lambda(\beta)) \neq 0$) iff it is induced by a
homeomorphism of $S$. As a corollary, we prove that if $K$ is a finite index
subgroup of $Mod_S^*$ and $f: K \to Mod_S^*$ is an injective homomorphism, then
$f$ is induced by a homeomorphism of $S$ and $f$ has a unique extension to an
automorphism of $Mod_S^*$.
