Let $I$ be a finite set, let $A = (a_{ij})_{i,j \in I}$ be an indecomposable symmetrizable generalized Cartan matrix of finite type, and let $\Gamma(A)$ be its Dynkin diagram. Let $G(A)$ denote the underlying undirected graph of $\Gamma(A)$, with vertex set $I$ and with an edge $\{i,j\}$ for $i \neq j$ exactly when $a_{ij}a_{ji} \neq 0$. Then $G(A)$ contains no simple cycle. Since $A$ is indecomposable, $G(A)$ is connected, so $G(A)$ is a tree.