Tutorial: Normalized Graph Laplacian

My Study on Graph & Normalized Laplacian Matrix

1. From Graph to Normalized Graph Laplacian

Graph is a node-edge representation, which can have many applications such as social media network.

A Graph Sample
A = np.array([[0, 1, 0, 0, 0],
[1, 0, 1, 1, 1],
[0, 1, 0, 1, 0],
[0, 1, 1, 0, 1],
[0, 1, 0, 1, 0]])
D = np.zeros((5,5))
for i in range(5):
D[i,i] = np.sum(A[i,:])
Degree Matrix D
L=D-A
Laplacian Matrix L
D2 = D
for i in range(5):
D2[i,i] = 1/np.sqrt(D2[i,i])
L2 = np.matmul(np.matmul(D2, L), D2)
Normalized Graph Laplacian

2. For Graph with Unequal Weighting Edges

Adjacent Matrix A
Degree Matrix D
Laplacian Matrix L
Normalized Graph Laplacian

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