Fun fact: the simplest edge detector is actually just [1 0 -1] (aka gradient(X(n))=X(n+1)-X(n-1)). To make sure you agree with your neighbors though, you could try to average with them by using the matrix [1 0 -1;1 0 -1;1 0 -1] (this is the prewitt filter). Then, to focus more on the center pixel, you can use sobel as above.
Fun fact: the simplest edge detector is actually just [1 0 -1] (aka gradient(X(n))=X(n+1)-X(n-1)). To make sure you agree with your neighbors though, you could try to average with them by using the matrix [1 0 -1;1 0 -1;1 0 -1] (this is the prewitt filter). Then, to focus more on the center pixel, you can use sobel as above.