#### Previous topic

scipy.sparse.csgraph.maximum_bipartite_matching

#### Next topic

scipy.sparse.csgraph.NegativeCycleError

# scipy.sparse.csgraph.structural_rank

`scipy.sparse.csgraph.``structural_rank`(graph)

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

  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.

  Parameters: | graph : sparse matrix Input sparse matrix.
  Returns: | rank : int The structural rank of the sparse graph. New in version 0.19.0.

  References

  [R15] | I. S. Duff, “Computing the Structural Index”, SIAM J. Alg. Disc. Meth., Vol. 7, 594 (1986).

  [R16] | http://www.cise.ufl.edu/research/sparse/matrices/legend.html