These graphs connect integers that form Pythagorean triples. With "triples" selected, two integers are connected if they form any two sides of a right triangle; thus, all Pythagorean triples appear as triangles in the graph. With "legs", two integers are connected if they constitute the two legs of a Pythagorean triple, and the edge between them is labeled with the corresponding hypotenuse. The graphs can show all triples or only primitive ones.

Pythagorean triples are sets of three integers that satisfy the Pythagorean equation , and thus form the side lengths of right triangles. In a primitive Pythagorean triple, the three integers have no factors in common.