# How to say with one word: “it has a tree structure”

• When objects relate to each other as pearls on a string (open, not closed), then we can say that the whole structure is "sequential" or "linear".

• The same way, we can call something "cyclic" if its elements are sequential, and the first is also connected to the last, like a necklace.

But is there a single adjective for expressing that some objects form a tree structure, like:

My only idea was "hierarchical", but that also implies that the root (starting point) of the tree is the most, and leaves are the least important, which isn't always the case.

• "Tree-structured"? – The Photon Jul 22 '17 at 22:24
• Perhaps "branched"? – Mark Hubbard Jul 22 '17 at 23:00
• I believe the term for this type of relational diagram is a "Parse tree". So I believe the term would be parsing or branching – PV22 Jul 22 '17 at 23:24
• tree-like, tree-shaped, arboreal – Drew Jul 23 '17 at 0:08
• I think "hierarchical" is still OK, despite the implications of importance - after all the "top" node in your diagram is generally called the "root" and the "bottom" nodes are "leaves". Tree structures are hierarchical :) – dimo414 Jul 23 '17 at 9:25

Dendritic

branching like a tree

Merriam Webster

• +1 If in doubt, Greek beats Latin – Hagen von Eitzen Jul 23 '17 at 18:51
• @bof how would this be different from his sequential and linear examples? – crobar Jul 24 '17 at 11:46
• That will be sure to confuse people. – dangph Jul 24 '17 at 12:30
• As interesting and accurate as this word is, it is pretty rare and will most likely not be understood. – Mitch Jul 24 '17 at 16:37
• It's used in biology and geology, but not in mathematics or computer science so far as I know. – dangph Jul 24 '17 at 23:59

You can call it "tree-like." Alternatively, you could describe it as "branching."

• +1 for an answer in plain English that will get the image across to most people, assuming many don't know enough Greek or Latin to decipher what "arboromorphic" or "dendritic" means (or at least need some time to stop and think about it). – CompuChip Jul 24 '17 at 7:33

Try arborescent:

resembling a tree in properties, growth, structure, or appearance

Merriam Webster

I like the term ramified (2, 3 - Free Dictionary) to describe something that develops into a branching or tree-like structure.

• Interesting. Unfortunately, I think the massive popularity of sense (1) in that definition is so overwhelming that most readers will think of it first even if they are aware of the other senses (and as a reader with a lot of background working with mathematical-type trees, I've never heard this word used to describe them, so suspect it is very likely to not be understood) – Jules Jul 23 '17 at 2:54
• Note that ramified already has a mathematical definition, which is a lot more specific than what the OP is going for. – Micah Jul 24 '17 at 15:27

Some people find it surprising that any (connected) acyclic structure can be treated as a tree, and even more surprising that any node in a given (connected) acyclic structure can be treated as the root node of a tree.

Often "hierarchical" has the connotations that there is one special privileged root node that is most important, and leaves are the least important.

When that connotation is unwanted, people often use the adjective "acyclic". There isn't anything special or more important about any one node in an acyclic graph, because every node works fine as a root node.

A few authors use "tree" as a synonym for any connected acyclic graph. Those authors use free tree or unrooted tree that does not yet have a root. Later, after a root node has been arbitrarily chosen, the structure becomes a "rooted tree".

A connected acyclic graph is known as a tree, and a possibly disconnected acyclic graph is known as a forest (i.e., a collection of trees). -- http://mathworld.wolfram.com/AcyclicGraph.html

and

A tree is a set of straight line segments connected at their ends containing no closed loops (cycles). In other words, it is a simple, undirected, connected, acyclic graph (or, equivalently, a connected forest). A tree with n nodes has n-1 graph edges. Conversely, a connected graph with n nodes and n-1 edges is a tree. Trees with no particular [root] node singled out are sometimes called free trees (or unrooted tree), by way of distinguishing them from rooted trees. -- http://mathworld.wolfram.com/Tree.html

There are many practical situations that involve some some possibly-cyclic connected graph, and a variety of algorithms have been developed to cut cycles (if any) until only the minimum spanning tree remains -- a connected acyclic graph.

After a (connected) acyclic graph is built, one person can arbitrarily pick any node as the root node, and treat the rest of the acyclic structure as a tree, with all the nodes directly connected to the chosen root node as the children of that root node, then all the remaining nodes directly connected to those children as the grandchildren of that root node, and so on for every level of descendants. A different person can arbitrarily pick some other node of that same acyclic graph as the root node, and use the same algorithm to build another rooted tree that is arranged differently than the first person's tree.

One adjective many would find acceptable is fractal. One dictionary definition, "a curve or geometric figure, each part of which has the same statistical character as the whole."

• There are implications here that are probably not wanted. Fractal in common usage usually implies "infinitely detailed", which would only be true of an infinitely large tree. Also, in technical use, it means "having a fractal dimension" or "non-integral capacity dimension" which is definitely not true of trees. – Jules Jul 23 '17 at 2:56