assuming you already know how convolutional NE network works from one perspective when we have an input image we just select a portion of this image like this 3x3 area and we know that each pixel is represented by a value between 0 and 255 and we also have a kernel that we know that each value in this kernel is updated by back propagation and how do we apply this kernel to this area we just simply multiply each value of the kernel by the corresponding value in the pixel and we sum all this up and we end up get a value like 600 and something but the question is important for us is where should we store this result when we look at the exact portion of this image but in the output feature map and the answer is we store it at the center and what about the other values which just convolve the kernel but you should already know this right an analogy of doing this but with with the graphs instead is that we are having a graph in a 3X3 grid structure we have one node at the center and all other nodes are pointed to this node at the center and what are each noes value this is just exactly the pixel value and what about the edges those are just the kernel values but let's just leave this 3. 11 behind and I will discuss it later so if I want to apply convolution with this graph instead I just do the same thing I just take a look at the value 48 of the of the note at the top left and multiply it by the edge which is 0. 12 and then I do it for the node at the top and the other node at the top right and all the other nodes and some these alter together and we end up getting a result and exactly like convolutional Network I replace this result by this value at the center and one way of intuitively looking at this is that each node in the neighborhood has some sort of information one has information 48 the other has information 109 and so on and so forth and since they're all pointed to this node at the center you're interested to pass their information so the Center node in next iteration is represented by a weighted average of the neighborhoods you can kind of consider the center node as yourself and all the nodes in the neighborhood as your friends and each friend has some influence on you which is represented by this age weights and the way you look over time would be different based on how your friends have influence on you but an issue that this approach has is that the way that you look currently has no effect on how you behave and the next iteration and this value of 52 is completely disregarded so how can we preserve that information we need to take consider this missing kernel 3.
11 and the way that we do it is that we just add a self Loop and the age value for this self Loop Edge is this exact 3. 1 and like before we multiply the value of 52 by this 3.
