Mathematica 8: EdgeList and CommunityStructureAssignment shadowing problem

Question

I'm facing some issues when trying to use the CommunityStructureAssignment function from the GraphUtilities package in Mathematica 8.

I'd like to output a community structure assignment for my random graph, but it seems the function is unrecognized by Mathematica. In particular with the following code I'm creating a random weighted graph G with 10 nodes and 30 edges and I visualize the weighted adjacency matrix:

nNodes = 10;
nEdges = 30;
G = Graph[EdgeList[RandomGraph[{nNodes, nEdges}]], EdgeWeight -> RandomReal[{0.1, 5}, nEdges]];

W = WeightedAdjacencyMatrix[G];
W // MatrixForm

After that, following the documentation of CommunityStructureAssignment, I'd imagine that feeding the EdgeList of G directly to CommunityStructureAssignment would result in a list but:

CommunityStructureAssignment[EdgeList[G], Weighted -> True]

returns it self:

CommunityStructureAssignment[{1 \[UndirectedEdge] 4, 
  1 \[UndirectedEdge] 5, 2 \[UndirectedEdge] 4, 2 \[UndirectedEdge] 5,
   2 \[UndirectedEdge] 1, 2 \[UndirectedEdge] 3, 
  3 \[UndirectedEdge] 5, 3 \[UndirectedEdge] 1, 4 \[UndirectedEdge] 5,
   4 \[UndirectedEdge] 3}, Weighted -> True]

while the documentation clearly says that:

g = {3 -> 2, 2 -> 1, 1 -> 3, 3 -> 5, 5 -> 6, 6 -> 7, 7 -> 5};
CommunityStructureAssignment[g]

should correctly work.

Now the question is: how can I feed the correct input graph into CommunityStructureAssignment? And also how to include the edge weights into the EdgeList?

Also I have to say, that once i import the GraphUtilities package, the definition of EdgeList turns red. Is this because there is a conflict of names?

Answer 1

I am using Mathematica 10 but I suppose the same issues will apply. I believe that the GraphUtilites package is not designed to work with Graph objects but instead other, earlier formats.

After loading Needs["GraphUtilities`"] the Symbol EdgeList is highlighted in red indicating shadowing, meaning that this Symbol exists in multiple contexts in the $ContextPath. If the one from the package context is used it does not recognize G:

GraphUtilities`EdgeList[G]

Likewise it seems that CommunityStructureAssignment does not recognize \[UndirectedEdge] as it was presumably written before the introduction of that functionality. If we use the System` EdgeList function and replace UndirectedEdge with Rule:

CommunityStructureAssignment[Rule @@@ System`EdgeList[G], Weighted -> True]

{1, 2, 3, 4, 2, 2, 2, 2, 2, 2}