graphresistor[g_, a_, b_] :=
  LinearSolve[
    SparseArray[{{a, a} -> 1, {i_, i_} :> Length@AdjacencyList[g, i],
      Alternatives @@ Join[#, Reverse /@ #] &[
        List @@@ EdgeList[VertexDelete[g, a]]] -> -1}, {VertexCount[
       g], VertexCount[g]}], SparseArray[b -> 1, VertexCount[g]]][[b]];
N[graphresistor[GridGraph[{10, 10}], 12, 77], 40]