EdgeWeight

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`EdgeWeight`

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is an option and annotation for Graph and related functions that specifies an edge weight.

Details

The following option settings can be used:

	Automatic	automatically determine edge weights
	{v_iv_j->w_ij,…}	edge has weight etc.
	{w₁,w₂,…}	give all edge weights in the same order as used by EdgeList
	{patternw,…}	edge that matches the pattern has weight w

The wrapper Annotation[v_iv_j,EdgeWeight->w] can be used when creating graphs in functions such as Graph etc.
The weight can be any expression.
The weight can be interpreted as cost or capacity, or can have other special meanings for different graph computation functions.

Examples

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

Set a weight for all edges:

In[1]:=1

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https://wolfram.com/xid/0rs1mxfky-8fxi6

Out[1]=1

The weighted adjacency matrix:

In[2]:=2

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https://wolfram.com/xid/0rs1mxfky-baprxk

Specify the weight for individual edges:

In[1]:=1

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https://wolfram.com/xid/0rs1mxfky-0kqh4

Out[1]=1

The list of edge weights in the order given in the graph:

In[2]:=2

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https://wolfram.com/xid/0rs1mxfky-occu4

Out[2]=2

Use any expression as a weight:

In[1]:=1

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https://wolfram.com/xid/0rs1mxfky-bcptub

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0rs1mxfky-fibbsw

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