of nested, alternating paths of nodes and edges. This simplifies representation and eliminates the overhead of assigning and using node identifiers. When discussing molecular trees, it's often useful to refer to node order (Figure ). An order is a property of a set that allows its members to be sorted through pairwise comparisons. Node order is the order in which the nodes of a molecular tree are added through depth-first construction. A node added before another node is said to "precede" it. A node added after another node is said to "succeed" it. In this way nodes can be prioritized. The root atom, uniquely lacking a parent, is ordered first because it precedes every other node. Similarly, a parent always precedes its children. Finally, the first child added to a given parent precedes all of its siblings. This relationship is transitive. If a node precedes (or succeeds) a sibling, then so do all of its descendants.