What you have drawn there is a recurrent model where there is a feedback loop. The only way that can work is if what you are feeding back into a layer/node is from the *previous* input/time-step, otherwise you've got an infinite loop.

You can certainly build something like that if you want you (2nd "layer" is an LSTM or RNN), however this is total overkill if all you are trying to do is build is a binary classifier. Depending on your input a single fully-connected layer may work, else add more layers.