Vassiliev knot invariants coming from Lie algebras and 4-invariants

We study the 4-bialgebra of graphs and the bialgebra of 4-invariants introduced by S.K.Lando. Our main goal is the investigation of the relationship between 4-invariants of graphs and weight systems arising in the theory of finite order invariants of knots. In particular, we show that the corank of the adjacency matrix of a graph leads to the weight system coming from the defining representation of the Lie algebra gl(N).