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IncidenceList[g,v]

gives a list of edges incident to vertex v.

IncidenceList[g,patt]

gives a list of edges incident to vertices that match the pattern patt.

IncidenceList[g,patt,d]

gives a list of incident edges d steps away.

IncidenceList[{vw,…},…]

uses rules vw to specify the graph g.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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IncidenceList

IncidenceList[g,v]

gives a list of edges incident to vertex v.

IncidenceList[g,patt]

gives a list of edges incident to vertices that match the pattern patt.

IncidenceList[g,patt,d]

gives a list of incident edges d steps away.

IncidenceList[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • IncidenceList is typically used to represent the incidence (or connection) between vertices and edges.
  • IncidenceList returns the list of edges in the order used by the graph g.

Examples

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Basic Examples  (3)

A list of edges incident to vertex 1:

Wolfram Language code: IncidenceList[[image], 1]

Find all vertices adjacent to vertices that match the pattern:

Wolfram Language code: IncidenceList[[image], _ ? (# < 3&)]

Highlight incidence edges:

Wolfram Language code: g = GridGraph[{9, 9}, VertexSize -> Medium, VertexStyle -> {41 -> Blue}];
Wolfram Language code: Table[HighlightGraph[g, IncidenceList[g, 41, i]], {i, 3}]

Scope  (6)

IncidenceList works with undirected graphs:

Wolfram Language code: IncidenceList[[image], 1]

Directed graphs:

Wolfram Language code: IncidenceList[[image], 1]

Use rules to specify the graph:

Wolfram Language code: IncidenceList[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}, 1]

Use patterns to obtain edges incident to a selected subset of vertices:

Wolfram Language code: IncidenceList[[image], Except[_Integer]]

Obtain incident edges d steps away from a vertex:

Wolfram Language code: IncidenceList[[image], 1, 2]

IncidenceList works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: IncidenceList[g, 50]//Timing

Properties & Relations  (2)

IncidenceList can be found using NeighborhoodGraph:

Wolfram Language code: g = [image];
Wolfram Language code: IncidenceList[g, 1]
Wolfram Language code: EdgeList[NeighborhoodGraph[g, 1], Except[1]]

AdjacencyList can be found using IncidenceList:

Wolfram Language code: g = [image];
Wolfram Language code: AdjacencyList[g, 2]
Wolfram Language code: DeleteCases[Flatten[List@@@IncidenceList[g, 2]], 2]
Wolfram Research (2012), IncidenceList, Wolfram Language function, https://reference.wolfram.com/language/ref/IncidenceList.html (updated 2015).

Text

Wolfram Research (2012), IncidenceList, Wolfram Language function, https://reference.wolfram.com/language/ref/IncidenceList.html (updated 2015).

CMS

Wolfram Language. 2012. "IncidenceList." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/IncidenceList.html.

APA

Wolfram Language. (2012). IncidenceList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IncidenceList.html

BibTeX

@misc{reference.wolfram_2026_incidencelist, author="Wolfram Research", title="{IncidenceList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/IncidenceList.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_incidencelist, organization={Wolfram Research}, title={IncidenceList}, year={2015}, url={https://reference.wolfram.com/language/ref/IncidenceList.html}, note=[Accessed: 12-June-2026]}