  A manifold $M^n$ inherits a labeled $n$-dimensional graph
$\widetilde{M}[G^L]$ structure consisting of its charts. This structure enables
one to characterize fundamental groups of manifolds, classify those of locally
compact manifolds with finite non-homotopic loops by that of labeled graphs
$G^L$. As a by-product, this approach also concludes that {\it every homotopy
$n$-sphere is homeomorphic to the sphere $S^n$ for an integer $n\geq 1$},
particularly, the Perelman's result for $n=3$.
