
Task

Given    10×10    grid nodes   (as shown in the image)   interconnected by    1Ω    resistors as shown,

find the resistance between points   A   and   B.



See also

   (humor, nerd sniping)   xkcd.com cartoon


ResistanceMatrix[g_Graph] := With[{n = VertexCount[g], km = KirchhoffMatrix[g]}, 
  Table[ ReplacePart[ Diagonal[ DrazinInverse[ ReplacePart[km, k -> UnitVector[n, k]]]], k -> 0], 
  {k, n}]
]
 
rm = ResistanceMatrix[GridGraph[{10, 10}]];
 
N[rm[[12, 68]], 40]