As far as I understand and looked into Attention Is All You Need and Transformer model for language understanding, the Self Attention at Scaled Dot-Product Attention is calculating $query$ and $key$ of the same word, which is the diagonal of the matrix in the diagram.
The $q \cdot k$ of the same word will generate the largest value, which means that a word attends to itself in a sentence. Is it correct or am I missing something?
Why Self Attention does not exclude the $q \cdot k$ of the same word itself?