DirectedNodeNetworks are simply NodeNetworks#1.3.6.1.4.1.33097.1.0.12 where the Edges#1.3.6.1.4.1.33097.1.0.12.1 are directional.
These are simply Nodes#1.3.6.1.4.1.33097.1.0.12.0 which do not have any Edges#1.3.6.1.4.1.33097.1.0.12.1 (references to) other Nodes#1.3.6.1.4.1.33097.1.0.12.0 but may be referenced by (have Edges#1.3.6.1.4.1.33097.1.0.12.1 from) other Nodes#1.3.6.1.4.1.33097.1.0.12.0.
Definition5.3.1. Let T be a tree. A vertex of T is said to be a leaf if its degree is 1. 2308.04512.pdf page 161
Also note this formal definition is from undirected Graphs#1.3.6.1.4.1.33097.1.0.14. This changes slightly because of the directed nature of DirectedNodeNetworks.
These are simply Nodes#1.3.6.1.4.1.33097.1.0.12.0 which are not referenced by (have Edges#1.3.6.1.4.1.33097.1.0.12.1 from) other Nodes#1.3.6.1.4.1.33097.1.0.12.0. OriginNodes may have Edges#1.3.6.1.4.1.33097.1.0.12.1 (references to) other Nodes#1.3.6.1.4.1.33097.1.0.12.0.
These are the same as the Root(r) of a Spanning Arborescence. However, I didn’t call them roots, as the root of something is usually a unique property.
Must have a unique, designated root ($r$) with in-degree 0.
DirectedNodeNetworks may be Acyclic#1.3.6.1.4.1.33097.1.0.12.7 like all NodeNetworks#1.3.6.1.4.1.33097.1.0.12.
https://en.wikipedia.org/wiki/Graph_theory
https://medium.com/basecs/a-gentle-introduction-to-graph-theory-77969829ead8