Image a circle of neurons. Each neuron is (or can) be connected to any other neuron. The weights between them can only be binary (0 or 1). What is this architecture called?

Edit: That should real "imagine", not "image".

Title says it all.

Let's imagine we have, say, 10 neurons, all in a circle. Now, each neuron can be connected to any other one, (except itself of course). However also crucially, the weights associated between every neurons can only ever be binary, that is to say, either 0 or 1.

What might this structure be called? As an aside, would the modeling of such a structure be possible with something like Theano, or Caffe?

Thanks!