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structural_rank(graph)

The structural rank of a matrix is the number of entries in the maximum transversal of the corresponding bipartite graph, and is an upper bound on the numerical rank of the matrix. A graph has full structural rank if it is possible to permute the elements to make the diagonal zero-free.

versionadded

Parameters

graph : sparse matrix

Input sparse matrix.

Returns

rank : int

The structural rank of the sparse graph.

Compute the structural rank of a graph (matrix) with a given sparsity pattern.

Examples

>>> 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) (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
See :

Back References

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scipy.sparse.csgraph._reordering.structural_rank

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