Return a minimum spanning tree of an undirected graph
A minimum spanning tree is a graph consisting of the subset of edges which together connect all connected nodes, while minimizing the total sum of weights on the edges. This is computed using the Kruskal algorithm.
Parameters :  csgraph: array_like or sparse matrix, 2 dimensions :
overwrite: bool, optional :


Returns :  span_tree: csr matrix :

Notes
This routine uses undirected graphs as input and output. That is, if graph[i, j] and graph[j, i] are both zero, then nodes i and j do not have an edge connecting them. If either is nonzero, then the two are connected by the minimum nonzero value of the two.
Examples
The following example shows the computation of a minimum spanning tree over a simple fourcomponent graph:
input graph minimum spanning tree
(0) (0)
/ \ /
3 8 3
/ \ /
(3)5(1) (3)5(1)
\ / /
6 2 2
\ / /
(2) (2)
It is easy to see from inspection that the minimum spanning tree involves removing the edges with weights 8 and 6. In compressed sparse representation, the solution looks like this:
>>> from scipy.sparse import csr_matrix
>>> from scipy.sparse.csgraph import minimum_spanning_tree
>>> X = csr_matrix([[0, 8, 0, 3],
... [0, 0, 2, 5],
... [0, 0, 0, 6],
... [0, 0, 0, 0]])
>>> Tcsr = minimum_spanning_tree(X)
>>> Tcsr.toarray().astype(int)
array([[0, 0, 0, 3],
[0, 0, 2, 5],
[0, 0, 0, 0],
[0, 0, 0, 0]])