absorbing_centrality.compute_fundamental_matrix

compute_fundamental_matrix(P, fast=True, drop_tol=1e-05, fill_factor=1000)[source]

Computes the fundamental matrix for an absorbing random walk.

Parameters:
  • P (scipy.sparse matrix) – The transition probability matrix of the absorbing random walk. To construct this matrix, you start from the original transition matrix and delete the rows that correspond to the absorbing nodes.
  • fast (bool, optional) –
  • True (default), use the iterative SuperLU solver from (If) –
  • scipy.sparse.linalg. –
  • drop_tol (float, optional) – If fast is True, the drop_tol parameter of the SuperLU solver is set to this value (default is 1e-5).
  • fill_factor (int, optional) – If If `fast is True, the fill_factor parameter of the SuperLU solver is set to this value (default is 1000).
Returns:

F – The fundamental matrix of the random walk. Element (i,j) holds the expected number of times the random walk will be in state j before absorption, when it starts from state i. For more information, check [1].
Return type:

scipy.sparse matrix

References

[1]Doyle, Peter G., and J. Laurie Snell. Random walks and electric networks. Carus mathematical monographs 22 (2000). https://math.dartmouth.edu/~doyle/docs/walks/walks.pdf