# Does a CNN have to be Fully Connected?

So I am trying to implement a specific CNN called a U-net. It states in page 3 that it doesn't have a fully connected layer.

Till then I understood CNN to have two stages; 1. Convolution, where the kernels are learnt and features are extracted and 2. where the extracted features are flattened and a Fully Connected Layer (FCL) is applied where weights and biases are learnt. This U-Net though has gotten me slightly confused and I wanted to make sure whether CNN need to be fully connected or not.

If they do not, then where does the 'neuron behaviour' come from in CNN? In what sense are they Neural Nets then?