To refine this definition in the light of the algebra of coupling of angular momenta (see below), a subdivision of the 3-connected graphs is helpful.
Ball-and-stick models of the graphs in another column of the table show the vertices and edges in the style of images of molecular bonds.
This is augmented by two additional rules: Since the starting vertex of the path is of no importance, the numbers in the representation may be cyclically permuted.
Often the anti-palindromic representations with are preferred (if they exist), and the redundant part is then replaced by a semicolon and a dash "; –".
Each 4-connected (in the above sense) simple cubic graph on 2n vertices defines a class of quantum mechanical 3n-j symbols.