Add weighted edge to a graph in Mathematica 8

Question

Is it possible to add an edge with a specific weight to a Mathematica Graph object? The function EdgeAdd has no option for the weights, nor the AddEdge function from the GraphUtilities package.

I want to modify the edge 1-4 of the CompleteGraph[5] for example, how should I do that?

Answer 1

For V9 and up. (you haven't specified your version in your question)

g = CompleteGraph[4]; 
PropertyValue[{g, UndirectedEdge[1, 2]}, EdgeWeight] = 2;
MatrixForm@Normal@WeightedAdjacencyMatrix[g]

$\left( \begin{array}{cccc} 0 & 2 & 1 & 1 \\ 2 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 \\ \end{array} \right)$

Answer 2

I'm not sure I quite understand what you intend to do with EdgeAdd thus I will only answer the "I want to modify the edge 1-4 of the CompleteGraph[5]" question.

Here I modify the edge 1 <-> 4 and 1 <-> 2 for generalisation purposes:

g = CompleteGraph[5];
weightsVal = {a, b}; (* in the same order as {1 <-> 4, 1 <-> 2}*)
weights = ReplacePart[Array[1 &, Length@EdgeList@g], 
  Rule @@@ Thread@{Flatten[Position[EdgeList@g, #] & /@ {1 <-> 4, 1 <-> 2}], weightsVal}]
Graph[EdgeList@g, AbsoluteOptions[g, VertexCoordinates], 
 EdgeWeight -> weights, 
 EdgeLabels -> Rule @@@ Thread@{EdgeList@g, weights}, 
 VertexLabels -> "Name", ImagePadding -> 10]
% // WeightedAdjacencyMatrix // MatrixForm

$\left( \begin{array}{ccccc} 0 & b & 1 & a & 1 \\ b & 0 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 \\ a & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \\ \end{array} \right)$