## Graph Laplacian

Tags: #machine learning #graph #GNN### Equation

$$L=I_{N}-D^{-\frac{1}{2}}AD^{-\frac{1}{2}} \\ L=U\Lambda U^{T}$$### Latex Code

L=I_{N}-D^{-\frac{1}{2}}AD^{-\frac{1}{2}} \\ L=U\Lambda U^{T}

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### Introduction

#### Equation

#### Latex Code

L=I_{N}-D^{-\frac{1}{2}}AD^{-\frac{1}{2}} \\ L=U\Lambda U^{T}

#### Explanation

Graph Laplacian matrix equals to the identity matrix I minus the matrix multiplication of three parts, the (-1/2) power of the degree matrix D, the adjacency matrix A, and (-1/2) power of degree matrix D. U is the eigenvectors of the normalized graph Laplacian L. The graph laplacian come from the graph Fourier transform F. The original signal x is first transformed to domain F(X) and inverse resulted signal is transformed back using the inverse graph Fourier transform F^{-1}.

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