UndirectedEdge

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`UndirectedEdge`

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UndirectedEdge[u,v] or uv

represents an undirected edge between u and v.

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UndirectedEdge[u,v,t] or u

v

represents an undirected edge between u and v with tag t.

Details

UndirectedEdge is also known as link or connection.
UndirectedEdge[u,v] can be input as uv. The character  is entered as ue or \[UndirectedEdge].
UndirectedEdge[u,v,t] can be input as uv. An empty template can entered as tue, and moves the cursor to the overscript position.

Examples

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Basic Examples (5)Summary of the most common use cases

Build a graph with undirected edges:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-gb1uwg

Out[1]=1

List of edges:

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-d1avng

Out[2]=2

Use ue to enter  directly:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-dkpjt3

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-lr0czz

Out[2]=2

Enter using a two-way rule <->:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-eyscbp

Out[1]=1

The two-way rules are converted to undirected edges:

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-balwtm

Out[2]=2

Style and label individual edges:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-ergo02

Out[1]=1

StandardForm formatting:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-hf39q7

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-l0q7xl

Out[2]=2

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

Use wrappers to specify edge properties, including style:

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-bbpjpo

Out[2]=2

Labels:

In[3]:=3

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https://wolfram.com/xid/0ywpsrfdca1w-g4vyjh

Out[3]=3

Interactive behavior:

In[4]:=4

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https://wolfram.com/xid/0ywpsrfdca1w-f448y

Out[4]=4

Wrappers can be used to specify any supported edge annotation:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-cyxk2u

Out[1]=1

As well as new ones:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-byy2yq

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-eabhy

Out[2]=2

Use UndirectedEdge to specify individual edges for options, including style:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-e5mot

Out[1]=1

Labels:

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-hnirp6

Out[2]=2

Use a list of edges to indicate which edges to highlight:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-c3sz0j

Out[1]=1

A subgraph:

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-bfnacd

Out[2]=2

Use edge patterns to select and count edges:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-calvzy

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-cn2j4u

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0ywpsrfdca1w-d96osv

Out[3]=3

Properties & Relations (3)Properties of the function, and connections to other functions

Use UndirectedEdge to construct undirected graphs:

In[5]:=5

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https://wolfram.com/xid/0ywpsrfdca1w-cvm4t2

Out[5]=5

Tree graphs:

In[6]:=6

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https://wolfram.com/xid/0ywpsrfdca1w-cnn4wi

Out[6]=6

Path graphs:

In[7]:=7

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https://wolfram.com/xid/0ywpsrfdca1w-b1r2oi

Out[7]=7

Inside graph constructors, TwoWayRule[a,b] is converted to UndirectedEdge[a,b]:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-etyvlt

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0ywpsrfdca1w-cql5gt

Out[2]=2

The adjacency matrix of an undirected graph is symmetric:

In[1]:=1

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https://wolfram.com/xid/0ywpsrfdca1w-bd6rdz

Out[1]=1

In[2]:=2

✖

https://wolfram.com/xid/0ywpsrfdca1w-b882g

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