# In a directed acyclic graph, what do you call the nodes with in-degree zero?

The question is in the title. What do you call "root nodes" in directed graphs. Is there a commonly accepted term? "Root" implies there's only one, which is not the case. I've scanned half a dozen glossaries before asking. I'm starting to suspect that no, there's no agreed moniker.

• A forest can have multiple roots, admittedly each tree has only one and in a forest every node belongs only to a single tree. Jan 10 at 4:09
• @Bergi not all graphs are trees. Directed graphs can have multiple sources, multiple "roots", and still be connected. Trees are a subset of directed acyclic graphs (only one root, and only one path to each node.) Jan 10 at 8:16
• Yes, I just wanted to add that in forests (a special case of DAGs) there is not only a single root, while "root" is still the commonly accepted term for them. Otherwise see Russel's answer. Jan 10 at 8:24

• @MichaelKay Actually it depends. From wikipedia I don't see any mention that the set $F$ of final states must be such that $\delta(s,x) = s$ or undefined for any $s \in F$ or that the initial state doesn't have incoming edges. In fact with Buchi automata and finite states commonly have outgoing edges since the definition for acceptance in that case involves states that are visited an infinite number of times while recognizing an $\omega$-word. Jan 10 at 14:59