absorbing_centrality.compute_fundamental_matrix¶
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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