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IncidenceList
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IncidenceList

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gives a list of edges incident to vertex v.

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IncidenceList[g,patt]

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

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IncidenceList[g,patt,d]

gives a list of incident edges d steps away.

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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

open allclose all

Basic Examples  (3)Summary of the most common use cases

A list of edges incident to vertex 1:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-tct9ln
Out[1]=1

Find all vertices adjacent to vertices that match the pattern:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-bjfw1t
Out[1]=1

Highlight incidence edges:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-pa9bjd
In[2]:=2
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https://wolfram.com/xid/01y2pwleray-i8oz7u
Out[2]=2

Scope  (6)Survey of the scope of standard use cases

IncidenceList works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-cf5x3
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-bfe6xi
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-bndh30
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-bp7bob
Out[1]=1

Obtain incident edges d steps away from a vertex:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-6u5205
Out[1]=1

IncidenceList works with large graphs:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-pq9ae
In[2]:=2
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https://wolfram.com/xid/01y2pwleray-hw7ms1
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

IncidenceList can be found using NeighborhoodGraph:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-hlzlm3
In[2]:=2
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https://wolfram.com/xid/01y2pwleray-c7ydwt
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/01y2pwleray-icuegl
Out[3]=3

AdjacencyList can be found using IncidenceList:

In[1]:=1
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https://wolfram.com/xid/01y2pwleray-mmi8
In[2]:=2
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https://wolfram.com/xid/01y2pwleray-hy6d54
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/01y2pwleray-k96tk5
Out[3]=3
Wolfram Research (2012), IncidenceList, Wolfram Language function, https://reference.wolfram.com/language/ref/IncidenceList.html (updated 2015).
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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).

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_incidencelist, author="Wolfram Research", title="{IncidenceList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/IncidenceList.html}", note=[Accessed: 25-March-2025 ]}

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@misc{reference.wolfram_2025_incidencelist, author="Wolfram Research", title="{IncidenceList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/IncidenceList.html}", note=[Accessed: 25-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_incidencelist, organization={Wolfram Research}, title={IncidenceList}, year={2015}, url={https://reference.wolfram.com/language/ref/IncidenceList.html}, note=[Accessed: 25-March-2025 ]}

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@online{reference.wolfram_2025_incidencelist, organization={Wolfram Research}, title={IncidenceList}, year={2015}, url={https://reference.wolfram.com/language/ref/IncidenceList.html}, note=[Accessed: 25-March-2025 ]}