scipy.sparse.csgraph.

structural_rank#

scipy.sparse.csgraph.structural_rank(graph)#

计算具有给定稀疏模式的图（矩阵）的结构秩。

矩阵的结构秩是对应二部图的最大横截中的条目数，并且是矩阵数值秩的上限。如果可以通过置换元素使对角线无零，则图具有满结构秩。

Added in version 0.19.0.

参数:

图稀疏矩阵: 输入稀疏矩阵。

返回:

等级整数: 稀疏图的结构等级。

参考文献

[1]

I. S. Duff, “Computing the Structural Index”, SIAM J. Alg. Disc. Meth., Vol. 7, 594 (1986).

[2]

http://www.cise.ufl.edu/research/sparse/matrices/legend.html

示例

>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import structural_rank

>>> graph = [
... [0, 1, 2, 0],
... [1, 0, 0, 1],
... [2, 0, 0, 3],
... [0, 1, 3, 0]
... ]
>>> graph = csr_matrix(graph)
>>> print(graph)
<Compressed Sparse Row sparse matrix of dtype 'int64'
    with 8 stored elements and shape (4, 4)>
    Coords  Values
    (0, 1)  1
    (0, 2)  2
    (1, 0)  1
    (1, 3)  1
    (2, 0)  2
    (2, 3)  3
    (3, 1)  1
    (3, 2)  3

>>> structural_rank(graph)
4