Editing Root system (section)

===Constructing the Dynkin diagram===

Given a root system, select a set Δ of [[root system#Positive roots and simple roots|simple roots]] as in the preceding section. The vertices of the associated Dynkin diagram correspond to the roots in Δ.  Edges are drawn between vertices as follows, according to the angles. (Note that the angle between simple roots is always at least 90 degrees.)
*No edge if the vectors are orthogonal,
*An undirected single edge if they make an angle of 120 degrees,
*A directed double edge if they make an angle of 135 degrees, and 
*A directed triple edge if they make an angle of 150 degrees.  
The term "directed edge" means that double and triple edges are marked with an arrow pointing toward the shorter vector. (Thinking of the arrow as a "greater than" sign makes it clear which way the arrow is supposed to point.)

Note that by the elementary properties of roots noted above, the rules for creating the Dynkin diagram can also be described as follows. No edge if the roots are orthogonal; for nonorthogonal roots, a single, double, or triple edge according to whether the length ratio of the longer to shorter is 1, <math>\sqrt 2</math>, <math>\sqrt 3</math>. In the case of the <math>G_2</math> root system for example, there are two simple roots at an angle of 150 degrees (with a length ratio of <math>\sqrt 3</math>). Thus, the Dynkin diagram has two vertices joined by a triple edge, with an arrow pointing from the vertex associated to the longer root to the other vertex. (In this case, the arrow is a bit redundant, since the diagram is equivalent whichever way the arrow goes.)