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In [1]:

    
import numpy as np
from scipy.sparse.csgraph import minimum_spanning_tree
from scipy.sparse import csr_matrix, coo_matrix, lil_matrix



In [2]:

    
l = [[0, 8, 0, 3],
     [0, 0, 2, 5],
     [0, 0, 0, 6],
     [0, 0, 0, 0]]



In [3]:

    
mst = minimum_spanning_tree(l)
print(mst)









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [4]:

    
print(type(mst))









    



<class 'scipy.sparse.csr.csr_matrix'>



In [5]:

    
print(mst.toarray())









    



[[0. 0. 0. 3.]
 [0. 0. 2. 5.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]]



In [6]:

    
print(mst.toarray().astype(int))



In [7]:

    
print(mst.astype(int).toarray())



In [8]:

    
a = np.array(l)
print(a)



In [9]:

    
print(type(a))









    



<class 'numpy.ndarray'>



In [10]:

    
print(minimum_spanning_tree(a))









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [11]:

    
csr = csr_matrix(l)
print(csr)









    



  (0, 1)	8
  (0, 3)	3
  (1, 2)	2
  (1, 3)	5
  (2, 3)	6



In [12]:

    
print(type(csr))









    



<class 'scipy.sparse.csr.csr_matrix'>



In [13]:

    
print(minimum_spanning_tree(csr))









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [14]:

    
print(minimum_spanning_tree(coo_matrix(l)))









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [15]:

    
print(minimum_spanning_tree(lil_matrix(l)))









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [16]:

    
n = 4
d = [8, 3, 2, 5, 6]
i = [0, 0, 1, 1, 2]
j = [1, 3, 2, 3, 3]



In [17]:

    
csr_ = csr_matrix((d, (i, j)), shape=(n, n))
print(csr_)









    



  (0, 1)	8
  (0, 3)	3
  (1, 2)	2
  (1, 3)	5
  (2, 3)	6



In [18]:

    
print(csr_.toarray())



In [19]:

    
print(minimum_spanning_tree(csr))









    



  (0, 3)	3.0
  (1, 2)	2.0
  (1, 3)	5.0



In [20]:

    
print(mst.toarray().astype(int).tolist())









    



[[0, 0, 0, 3], [0, 0, 2, 5], [0, 0, 0, 0], [0, 0, 0, 0]]



In [21]:

    
print(type(mst.toarray().astype(int).tolist()))









    



<class 'list'>



In [22]:

    
print(mst.sum())



In [23]:

    
print(int(mst.sum()))



In [24]:

    
r, c = mst.nonzero()
print(r, c)









    



[0 1 1] [3 2 3]



In [25]:

    
print(list(zip(*mst.nonzero())))









    



[(0, 3), (1, 2), (1, 3)]



In [26]:

    
print(mst.data)









    



[3. 2. 5.]



In [27]:

    
print(list(zip(*mst.nonzero(), mst.data.astype(int))))









    



[(0, 3, 3), (1, 2, 2), (1, 3, 5)]



In [28]:

    
l = [[0, 8, 0, 3],
     [8, 0, 2, 5],
     [0, 2, 0, 6],
     [3, 5, 6, 0]]



In [29]:

    
print(minimum_spanning_tree(l).toarray().astype(int))



In [30]:

    
l = [[0, 8, 0, 3],
     [100, 0, 2, 5],
     [100, 100, 0, 6],
     [100, 100, 100, 0]]



In [31]:

    
print(minimum_spanning_tree(l).toarray().astype(int))



In [32]:

    
l = [[0, 8, 0, 3],
     [0, 0, 100, 5],
     [0, 2, 0, 6],
     [0, 0, 0, 0]]



In [33]:

    
print(minimum_spanning_tree(l).toarray().astype(int))