Lemma 2

Tag 0AY3, permanent. Cite it as [Bourbaki, Tag 0AY3].

Lie Groups and Lie Algebras, chapter VI, § 4. Classification of root systems

Any vertex of $X$ belongs to at most 3 edges.

Indeed, if $i$ is linked to $h$ other vertices, the relations $q_{ij}^2 \geq \frac{1}{4}$ for these other vertices implies that $\frac{h}{4} < 1$ by Lemma 1, so $h \leq 3$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Exercise 11, § 4
Lemma 10, § 4
Lemma 7, § 4

Cites

Lemma 1