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TreeLevel[tree,levelspec]

gives a list of all subtrees of tree on levels specified by levelspec.

TreeLevel[tree,levelspecelem]

gives a list of the element elem of subtrees on levels specified by levelspec.

TreeLevel[levelspec]

represents an operator form of TreeLevel that can be applied to a tree.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Level Specifications  
Elements  
Options  
TreeTraversalOrder  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
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TreeLevel

TreeLevel[tree,levelspec]

gives a list of all subtrees of tree on levels specified by levelspec.

TreeLevel[tree,levelspecelem]

gives a list of the element elem of subtrees on levels specified by levelspec.

TreeLevel[levelspec]

represents an operator form of TreeLevel that can be applied to a tree.

Details and Options

  • TreeLevel lists the subtrees on any range of levels in a Tree object. The list of subtrees can be given in many different orders, including depth-first and breadth-first traversals.
  • TreeLevel[tree,levelspec] gives a list of the subtrees on the given levels. This can also be expressed as TreeLevel[tree,levelspec"Subtree"].
  • TreeLevel[tree,levelspec"Data"] gives a list of the data on the given levels.
  • TreeLevel uses standard level specifications:
  • nlevels 1 through n
    Alllevels 0 through Infinity
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
    "Leaves"level -1 only
    "NonLeaves"levels 0 through -2
  • A positive level n+1 consists of all subtrees of tree that are children of subtrees on level n.
  • Level 0 corresponds to the root of the tree.
  • Level -1 corresponds to the leaves.
  • A negative level -(n+1) consists of all subtrees whose children are on levels -1, -2, …, -n, with highest level -n.
  • TreeLevel traverses subtrees in a left-to-right, depth-first order, with children visited before their parents.
  • TreeLevel[…,TreeTraversalOrderorder] allows visiting subtrees in different orders, such as depth-first and breadth-first traversals.
  • TreeLevel[levelspec][tree] is equivalent to TreeLevel[tree,levelspec].

Examples

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Basic Examples  (3)

Extract the subtrees on the second level:

Wolfram Language code: TreeLevel[[image], {2}]

Extract the data on a range of levels:

Wolfram Language code: TreeLevel[[image], {1, -2} -> "Data"]

Use the operator form of TreeLevel:

Wolfram Language code: TreeLevel[{1, 3}][[image]]

Scope  (8)

Level Specifications  (7)

Extract the subtrees on all levels:

Wolfram Language code: TreeLevel[[image], All]

Extract the subtrees on levels 1, 2 and 3:

Wolfram Language code: tree = [image];
Wolfram Language code: TreeLevel[tree, 3]

Extract the subtrees only on level 3:

Wolfram Language code: TreeLevel[tree, {3}]

Extract levels 0 through 2:

Wolfram Language code: TreeLevel[tree, {0, 2}]

Extract all levels, starting at level 1:

Wolfram Language code: TreeLevel[[image], Infinity]

Extract also level 0:

Wolfram Language code: TreeLevel[[image], {0, Infinity}]

Negative levels:

Wolfram Language code: tree = [image];
Wolfram Language code: TreeLevel[tree, -1]
Wolfram Language code: TreeLevel[tree, -2]
Wolfram Language code: TreeLevel[tree, {-2}]

Positive and negative levels can be mixed:

Wolfram Language code: TreeLevel[[image], {1, -1}]

Extract the leaves:

Wolfram Language code: TreeLevel[[image], "Leaves"]

Extract the non-leaves:

Wolfram Language code: TreeLevel[[image], "NonLeaves"]

Use TreeLevel as an operator form in a tree position specification:

Wolfram Language code: TreeExtract[[image], {2, TreeLevel[{1}]}]

Elements  (1)

Extract the subtrees (default):

Wolfram Language code: TreeLevel[[image], 1 -> "Subtree"]

Extract the data:

Wolfram Language code: TreeLevel[[image], 1 -> "Data"]

Options  (3)

TreeTraversalOrder  (3)

By default, subtrees are listed in a depth-first order, with parents visited after their children:

Wolfram Language code: TreeLevel[[image], All, TreeTraversalOrder -> "DepthFirst"]

Specify a top-down, right-to-left variant:

Wolfram Language code: TreeLevel[[image], All, TreeTraversalOrder -> {"DepthFirst", "TopDown", "RightLeft"}]

List subtrees in a breadth-first order, with nodes on the same level from the root visited before the nodes on the next level:

Wolfram Language code: TreeLevel[[image], All, TreeTraversalOrder -> "BreadthFirst"]

List subtrees in a leaves-first order, with nodes on the same level from the leaves visited before the nodes on the next level:

Wolfram Language code: TreeLevel[[image], All, TreeTraversalOrder -> "LeavesFirst"]

Applications  (2)

Extract subtrees at successive levels from the root:

Wolfram Language code: Table[TreeLevel[[image], {n}], {n, 0, 5}]

Extract subtrees at successive levels from the bottom:

Wolfram Language code: Table[TreeLevel[[image], {-n}], {n, 1, 6}]

Properties & Relations  (4)

TreeLevel[tree,levelspec] is equivalent to TreeChildren@TreeExtract[tree,TreeLevel[levelspec]]:

Wolfram Language code: tree = RandomTree[16]
Wolfram Language code: TreeLevel[tree, {2, 4}]
Wolfram Language code: % === TreeChildren@TreeExtract[tree, TreeLevel[{2, 4}]]

Level[expr,levelspec] is equivalent to TreeLevel[ExpressionTree[expr,"Subexpressions"],levelspec"Data"]:

Wolfram Language code: Level[a[b[c, d[e, f]], g[h]], {0, -2}]
Wolfram Language code: ExpressionTree[a[b[c, d[e, f]], g[h]], "Subexpressions"]
Wolfram Language code: TreeLevel[%, {0, -2} -> "Data"]

Level[expr,levelspec,HeadsTrue] is equivalent to TreeLevel[ExpressionTree[expr,"Subexpressions",HeadsTrue],levelspec"Data"] for positive levels:

Wolfram Language code: Level[f[g, h][a, b, c], {1, 2}, Heads -> True]
Wolfram Language code: ExpressionTree[f[g, h][a, b, c], "Subexpressions", Heads -> True]
Wolfram Language code: TreeLevel[%, {1, 2} -> "Data"]

TreeLeaves gives the subtrees at level -1:

Wolfram Language code: tree = [image];
Wolfram Language code: TreeLeaves[tree] === TreeLevel[tree, {-1}]

Possible Issues  (1)

TreeLevel by default starts at level 1, so does not extract the whole tree:

Wolfram Language code: TreeLevel[[image], -1]
Wolfram Language code: TreeLevel[[image], {0, -1}]
Wolfram Research (2021), TreeLevel, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeLevel.html (updated 2022).

Text

Wolfram Research (2021), TreeLevel, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeLevel.html (updated 2022).

CMS

Wolfram Language. 2021. "TreeLevel." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/TreeLevel.html.

APA

Wolfram Language. (2021). TreeLevel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TreeLevel.html

BibTeX

@misc{reference.wolfram_2026_treelevel, author="Wolfram Research", title="{TreeLevel}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/TreeLevel.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_treelevel, organization={Wolfram Research}, title={TreeLevel}, year={2022}, url={https://reference.wolfram.com/language/ref/TreeLevel.html}, note=[Accessed: 13-June-2026]}