In [77]: L = np.array([[2, -1, -1, 0, 0], [-1, 3, -1, -1, 0], [-1, -1, 3, -1, 0]
...: , [0, -1, -1, 3, -1], [0, 0, 0, -1, 1]])
In [78]: vals, vecs = np.linalg.eig(L)
In [79]: vals
Out[79]: array([ 0. , 0.82991351, 2.68889218, 4.4811943 , 4. ])
In [80]: vecs
Out[80]:
array([[ 4.47213595e-01, 4.37531395e-01, -7.03081478e-01,
-3.37998097e-01, -1.24491566e-16],
[ 4.47213595e-01, 2.55974786e-01, 2.42173667e-01,
4.19319477e-01, 7.07106781e-01],
[ 4.47213595e-01, 2.55974786e-01, 2.42173667e-01,
4.19319477e-01, -7.07106781e-01],
[ 4.47213595e-01, -1.38018756e-01, 5.36249932e-01,
-7.02415001e-01, -8.17563909e-16],
[ 4.47213595e-01, -8.11462211e-01, -3.17515788e-01,
2.01774144e-01, 3.46536171e-16]])
In [81]: vecs[:, 0]
Out[81]: array([ 0.4472136, 0.4472136, 0.4472136, 0.4472136, 0.4472136])
In [82]: vecs[:, 1]
Out[82]: array([ 0.43753139, 0.25597479, 0.25597479, -0.13801876, -0.81146221])
In [83]: vecs[:, 3]
Out[83]: array([-0.3379981 , 0.41931948, 0.41931948, -0.702415 , 0.20177414])
In [84]: vals
Out[84]: array([ 0. , 0.82991351, 2.68889218, 4.4811943 , 4. ])