Graph Convolution vs$.$ Convolution

The node update equation for a Graph Convolution layer is given by:

$h_u^{(l+1)}=(b^{(l)}+{\displaystyle \underset{\text{v}\text{i}\text{n}\text{N}(u)}{\overset{?}{}}}\frac{1}{c_{u,v}}{W}^{(l)}{h}_v^{(l)})$

where,

$$ u is the node

$$ l is the layer

$$ b is the bias

$$ W is the trainable parameter matrix

$$ h$^(0)$ is the node feature.

A $2$D Convolution layer without kernel flipping is given by:

$S^{(l+1)}(i,j)=((S^{(l)}*K^{(l)})(i,j)+b^{(l)})$

$=({\displaystyle \underset{m}{\overset{?}{}}}{\displaystyle \underset{n}{\overset{?}{}}}{S}^{(l)}(i+m,j+n)K^{(l)}(m,n)+b^{(l)}),$

where,

$$ S is the feature map

$$ K is the kernel

$$ Here, S$^(0)=$ I $($i$.$e$.$ original image$).$

NOTE: For simplicity, set the biases to $0.$

Describe a graph that is equivalent to an image $.$

Include all the details and technicalities $($e$.$g$.,$ which components are equivalent, node connectivity, edge

cases, exceptions, indexing$).$ An illustration could help but grading will be solely based on the description.

Anything that is part of the illustration that is not described in words will not count as a point.