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I have a graph with weighted edges, and I'd like to obtain the edge weights of the edges in the graph. Is there a nicer way of doing this than getting the WeightedAdjacencyMatrix of the graph? A list of weights that's 1-1 with the EdgeList of the graph would be great.

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@R.M the EdgeList doc page says "Edges in EdgeList are given in the same order they are entered for Graph" – Sjoerd C. de Vries Apr 13 '12 at 22:27
@R.M Exactly the same problem exists with WeightedAdjacencyMatrix[]. How do you know which vertex is in which rol/col? Well, you know because the help states that "The vertices Subscript[v, i] are assumed to be in the order given by VertexList[g]" – Dr. belisarius Apr 14 '12 at 14:24
@belisarius Ha! You can clearly tell I don't work much with graph objects ;) I'm removing my comment – R. M. Apr 14 '12 at 15:08
@R.M Neither do I. But I was bitten a few times by these doubts :) – Dr. belisarius Apr 14 '12 at 15:26
I have spent far too much time trying to understand the role played by a vertex's list position as opposed to the vertex's "name." If one's vertex "names" are consecutive integers, everything works pretty much as expected. The difficulty starts for me when I use MorphologicalGraph, which returns a graph having non-consecutive integer "names" assigned to the vertices. In fact, for MorphologicalGraph, the vertex names constitute a permutation of Range[n]. Hey, what's so confusing about that? Cheer up -- there are only (n! - 1) ways you can be wrong. Hint: use VertexIndex to get back to reality. – Ralph Dratman Jul 15 '12 at 2:20
up vote 3 down vote accepted

You can still use WeightedAdjacencyMatrix and massage the output to a nicer form —

g = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, EdgeWeight -> {2, 3, 4}];
    {x_, y_} :> UndirectedEdge[x, y], {2}]

enter image description here

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g = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, EdgeWeight -> {2, 3, 4}];
AbsoluteOptions[g, EdgeWeight] /. HoldPattern[EdgeWeight -> x_] -> x
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+1 How does HoldPattern work here? Any reason for not using AbsoluteOptions[g, EdgeWeight][[1, 2]] or /. (EdgeWeight -> x_) :> x ? – DavidC Apr 13 '12 at 23:46
@David Nahhh just an old vice – Dr. belisarius Apr 14 '12 at 4:50

Using PropertyValue[g,property] and Thread or Map:

    g = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 1}, EdgeWeight -> {2, 3, 4}];
    Thread[EdgeList[g] -> PropertyValue[g, EdgeWeight]] 
    Map[# -> PropertyValue[{g, #}, EdgeWeight] &, EdgeList[g]]

both give:

enter image description here

Similarly, use

   Thread[{EdgeList[g], PropertyValue[g, EdgeWeight]}] 
   Map[{#, PropertyValue[{g, #}, EdgeWeight]} &, EdgeList[g]]

to get a list:

enter image description here

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