I am having trouble to know what is the formal mathematical way to in which we define what is a sparse matrix. I know that a sparse matrix, is a matrix in which most of the elements are zero. But by most are we saying 50% of the elements are zero?
I don't think there is an 'official' or 'formal' break point where a graph becomes sparse. You generally speak of a sparse matrix when the sparsity of the matrix is noteworthy, and especially if it allows you to apply special computational techniques that only work on matrices with many zero entries.