# Visualising pseudo-tree with two parents per node

I have an algorithm that recursively connects together pairs of nodes into new nodes. It looks like the Huffman code algorithm, except that a node can be re-used after it has been part of a merge. The result is a graph where each node has two parents, but can have any amount of children.

Is there a term for such a graph? It isn't technically a tree -- and has none of the special properties of a tree -- but it does look very related to one, which makes me think someone has explored this kind of generalisation. A pseudo-tree? A multi-parent tree?

The reason I ask is because it's easy to find tree drawing software out there (e.g. ETE3, which seems like it only supports binary trees), but searching for "graph visualisation" gives way too general results (e.g. for social network analysis).

Example, drawn manually:

• What is the parent relationship and how does it relate to the merging? Why can a node have multiple children?
– D.W.
Dec 20, 2022 at 19:44
• @D.W. The relationship is string concatenation. A node can have multiple children because it can be concatenated to multiple strings.
– Mew
Dec 21, 2022 at 12:01
• I don't understand. I don't understand what you mean by "concatenated to multiple strings" - the question says nothing about strings or about concatenation. Can you please edit the question to define precisely the conditions under which one node is considered to be a parent of another node? Can you give an example of a minimal sequence of merges that leads to a node having two or more children?
– D.W.
Dec 21, 2022 at 21:42
• @D.W. Haha, the question was abstract because I wanted to keep it as graph-theoretical as possible. The example relation I gave was not in the question because it was only relevant as an answer to your question. Anyways, I've added an example graph. The question isn't why this relation exists, but what one calls it.
– Mew
Dec 21, 2022 at 22:35