The classification of the evolutions of nodal points. The classification is based on the first column, that is n λ ( k 0 ) and n ( k 0 ) . The second and third columns show the constraints of the band dispersion around the NP and the possible geometry forms of the nodal line in k_x–k_y–(λ space passing the NP, respectively. The last column shows the possible evolutions of NPs under a general form of perturbations. One can notice that the Dirac point (with linear dispersion along every direction) is stable against any chiral symmetric perturbation and cannot disappear nor transit to multi-NPs.