I am not tremendously familiar with electrical circuits (I have some memories, but too long ago) and now I have come accross a problem where I need to compute the resistance distance in a graph.
So, given a circuit of resistances (for instance a grid of resistances) I found the definition of the resistance distance in Wikipedia and here Confused on Calculating Resistance Distance Matrix But in BOTH cases, the resistances are all of 1 Ohm.
Is it possible to apply the same formula when the resistance values are different from one another? If not, what formula am I looking for?
Also, so I understand the overall concept: this would allow me to chose two points x and y in the circuit, and know what equivalent value of resitance I would need to wire directly between them to have an equivalent network, right?
In terms of scale, how well does computing this distances scale? Say I have 1million crossings/nodes. Is the matrix computation fast enough or do physicist have some trick to accelerate calculations?