Let $\Gamma$ be a finite connected simple graph, and let $C_\Gamma$ be the symmetric matrix indexed by the vertices of $\Gamma$ and defined by
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\begin{align*}
(C_\Gamma)_{vv} &= 2,\\
(C_\Gamma)_{vw} &= -1 \quad \text{if } v \text{ and } w \text{ are adjacent in } \Gamma,\\
(C_\Gamma)_{vw} &= 0 \quad \text{if } v \ne w \text{ and } v,w \text{ are not adjacent in } \Gamma.
\end{align*}
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If $C_\Gamma$ is positive definite, then $\Gamma$ is isomorphic to exactly one of the Dynkin diagrams
Conversely, each of the graphs $A_\ell$ for $\ell \ge 1$, $D_\ell$ for $\ell \ge 4$, and $E_6,E_7,E_8$ occurs as the Dynkin diagram of a finite reduced crystallographic root system.