connected_cmatrix(C, directed=True, lcc=None)¶
Compute the count matrix on the largest connected set.
- C (scipy.sparse matrix) – Count matrix specifying edge weights.
- directed (bool, optional) – Whether to compute connected components for a directed or undirected graph. Default is True
- lcc ((M,) ndarray, optional) – The largest connected set
C_cc – Count matrix of largest completely connected set of vertices (states)
Viewing the count matrix as the adjacency matrix of a (directed) graph the larest connected submatrix is the adjacency matrix of the largest connected set of the corresponding graph. The largest connected submatrix can be efficiently computed using Tarjan’s algorithm.
 Tarjan, R E. 1972. Depth-first search and linear graph algorithms. SIAM Journal on Computing 1 (2): 146-160.
>>> import numpy as np >>> from msmtools.estimation import largest_connected_submatrix
>>> C = np.array([[10, 1, 0], [2, 0, 3], [0, 0, 4]])
>>> C_cc_directed = largest_connected_submatrix(C) >>> C_cc_directed array([[10, 1], [ 2, 0]]...)
>>> C_cc_undirected = largest_connected_submatrix(C, directed=False) >>> C_cc_undirected array([[10, 1, 0], [ 2, 0, 3], [ 0, 0, 4]]...)