  In 2004, Carter, Elhamdadi and Saito defined a homology theory for
set-theoretic Yang-Baxter operators(we will call it the "algebraic" version in
this article). In 2012, Przytycki defined another homology theory for
pre-Yang-Baxter operators which has a nice graphic visualization(we will call
it the "graphic" version in this article). We show that they are equivalent.
The "graphic" homology is also defined for pre-Yang-Baxter operators, and we
give some examples of it's one-term and two-term homologies. In the two-term
case, we have found torsion in homology of Yang-Baxter operator that yields the
Jones polynomial.
