How to obtain the resistance distance matrix of a graph?
I tried to compute resistance distance matrix of a graph g by first evaluating the Moore-Penrose inverse of the Laplacian matrix, but the result is not accurate, the entries are slightly different. I tried with the following algorithm.
L=g.laplacian_matrix()
from scipy import linalg
M=matrix(linalg.pinv(L))
R=matrix(QQ, g.order())
for i in range(g.order()):
for j in range(g.order()):
if i!=j:
R[i,j]=M[i,i]+M[j,j] -M[i,j]-M[j,i]
What do you mean by "not accurate"?
Why did you write
from scipy import linalg?I imagine that scipy does not convert the pseudo-inverse exactly. Anyhow, please specify the example of a graph on which you see the problem.
For any tree classical distance matrix and resistance distance matrices are same. But the above program is giving me slightly different values. for example instead of 3, it gives 3.002176 for all the entries. I think its because linalg.pinv(L) does not give the accurate g-inverse.
Indeed, scipy works mostly with floating point numbers (= finite precision)