Four approaches to construct polynomial invariants for trivalent knotted graphs in S3 are compared. The first approach is based on vertex model with R-matrices and Glebsh-Gordan coefficients, appearing in SLq(2)-representations theory, as Boltzman weights. The second approach is based on Kauffman's quantum spin network theory, the third one is based on Witten-Turaev area-coloring model (or face model) based on quantum 6j-symbols, where q is root of unity. The fourth approach is based on the same face (or area-coloring) model, but q is not root of unity. The coincidence (up to certain normalization) of topological invariants, arising from these four state models, is proved.