Figure : Increasingly restrictive join operators. While a join allows any nodes of two subgraphs to be linked, for a cut node preserving join only connections between nodes involved in the cut sets of their respective parental graphs are permitted. A degree preserving join further requires all nodes of the offspring graph to adhere to the degree of their respective parental vertices. The most restrictive join presented is the natural join, which introduces edge weights, e.g. bond orders, that must be conserved.