The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra \({\vec {\mathcal{G}}}\) of acyclic arrow graphs (modulo an oriented version \(\overrightarrow {STU} \) of the STU relation). The algebra \({\vec {\mathcal{G}}}\) encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented \(\overrightarrow {AS} \) and \(\overrightarrow {IHX} \) relations hold, and that \({\vec {\mathcal{G}}}\) is isomorphic to the algebra \({\vec {\mathcal{A}}}\) of arrow diagrams. As an application, we consider an appropriate link-homotopy version \(\vec {\mathcal{A}}^h \) of the algebra \({\vec {\mathcal{A}}}\). Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra \(\vec {\mathcal{A}}^h \) and in ℝ. We observe that this construction gives the ‘universal’ Milnor's link-homotopy μ-invariants.