WOLFRAM

Wolfram Language & System Documentation Center

ArrayComponents[array]

gives an array in which all identical elements of array are replaced by an integer index representing the component in which the element lies.

ArrayComponents[array,level]

finds the identical elements at the specified level in array

ArrayComponents[array,level,rules]

uses a rule or a list of rules for specifying the labels.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
See Also
Related Guides
History
Cite this Page

ArrayComponents

ArrayComponents[array]

gives an array in which all identical elements of array are replaced by an integer index representing the component in which the element lies.

ArrayComponents[array,level]

finds the identical elements at the specified level in array

ArrayComponents[array,level,rules]

uses a rule or a list of rules for specifying the labels.

Details

  • ArrayComponents returns a label matrix where identical elements are represented by consecutive non-negative integers.
  • Occurrences of zeros or None in array are always labeled with zeros.
  • ArrayComponents can be used to canonicalize label matrices.

Examples

open all close all

Basic Examples  (3)

Components in a symbolic array:

Wolfram Language code: ArrayComponents[(⁠| | | | | | - | - | - | - | | 0 | a | a | a | | 0 | a | a | a | | 0 | a | a | a | | b | b | b | b |⁠), 2]//MatrixForm

Components in the first level of an array:

Wolfram Language code: ArrayComponents[(⁠| | | | | | - | - | - | - | | 0 | a | a | a | | 0 | a | a | a | | 0 | a | a | a | | b | b | b | b |⁠), 1]

Label identical elements in a list:

Wolfram Language code: ArrayComponents[{8, 2.5, 7, 8}]

Scope  (3)

ArrayComponents works with arbitrarily nested lists of symbols:

Wolfram Language code: ArrayComponents[{{True, False}, x, {10, 10}, {True, x, {False}}}]

Label all positive integers with a specific label:

Wolfram Language code: ArrayComponents[(⁠| | | | | | - | - | - | - | | 0 | a | a | a | | 0 | a | a | a | | 0 | a | a | a | | 1 | 2 | 3 | 4 |⁠), 2, n_Integer ? Positive -> -1]//MatrixForm

Use a specific label for a component:

Wolfram Language code: ArrayComponents[(⁠| | | | | | - | - | - | - | | 0 | a | a | a | | 0 | a | b | c | | 0 | a | a | d | | e | e | e | e |⁠), 2, a -> 0]//MatrixForm

Applications  (1)

Normalize a label matrix with missing labels:

Wolfram Language code: m = DeleteSmallComponents[WatershedComponents[[image]]]; {Max[m], Max[ArrayComponents[m]], Length[Tally[Select[Flatten@m, Positive]]]}
Wolfram Research (2010), ArrayComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayComponents.html (updated 2012).

Text

Wolfram Research (2010), ArrayComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayComponents.html (updated 2012).

CMS

Wolfram Language. 2010. "ArrayComponents." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/ArrayComponents.html.

APA

Wolfram Language. (2010). ArrayComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArrayComponents.html

BibTeX

@misc{reference.wolfram_2026_arraycomponents, author="Wolfram Research", title="{ArrayComponents}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayComponents.html}", note=[Accessed: 15-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_arraycomponents, organization={Wolfram Research}, title={ArrayComponents}, year={2012}, url={https://reference.wolfram.com/language/ref/ArrayComponents.html}, note=[Accessed: 15-June-2026]}