  A general technique for the study of embedded quantum graphs with magnetic
fields and spin-orbit interaction is presented. The analysis is used to
understand the contribution of Rashba constant to the extreme localization
induced by magnetic field in the T3 shaped quantum graph. We show that this
effect is destroyed at generic values of the Rashba constant. On the other
hand, for certain combinations of the Rashba constant and the magnetic
parameters another series of infinitely degenerate eigenvalues appears.
