Efficient Implementation of Resistance Distance for graphs?

Question

Is there an implementation of the resistance distance matrix (or just resistance matrix) for graphs available in Mathematica?

Answer 1

Based on the definition from the Wikipedia article, this should give you the resistance distance matrix of the graph g:

With[{Γ = PseudoInverse[KirchhoffMatrix[g]]},
 Outer[Plus, Diagonal[Γ], Diagonal[Γ]] - Γ - Transpose[Γ]
]

Answer 2

This is based on 2012rcampion's answer.

GraphResistanceMatrix[g_?GraphQ] := 
 Module[{kirchhoffMatrix, pseudoInverse, diagonal}, 
  kirchhoffMatrix = KirchhoffMatrix[g]; 
  pseudoInverse = PseudoInverse[kirchhoffMatrix];
  diagonal = Diagonal[pseudoInverse];
  SparseArray[
   Outer[Plus, diagonal, diagonal] - pseudoInverse - 
    Transpose[pseudoInverse]]]

To test this I did

data = EntityValue[
  FilteredEntityClass["Graph", 
   EntityFunction[graph, graph["VertexCount"] === 21]], 
  "ResistanceMatrix", "NonMissingEntityAssociation"]

Then I did

CheckResistanceMatrix = GraphResistanceMatrix[Graph[#1]] === #2 &;

Then I did

KeyValueMap[CheckResistanceMatrix][data]

and all the values from GraphResistanceMatrix matched GraphData's precomputed "ResistanceMatrix" value.