Construction of some algebras associated to directed graphs and related   to factorizations of noncommutative polynomials
  This is a survey of recently published results. We introduce and study a wide class algebras associated to directed graphs and related to factorizations of noncommutative polynomials. In particular, we show that for many well-known graphs such algebras are Koszul and compute their Hilbert series. 
Vladimir Retakh, Shirlei Serconek and Robert Lee Wilson