Distinct eigenvalues are realizable with generic eigenvectors

Motivated by applications in matrix constructions used the inverse eigenvalue problem for graphs, we study a concept of genericity eigenvectors associated with given spectrum and connected graph. This generalizes established notion nowhere-zero eigenbasis. Given any simple graph G on n vertices no multiple eigenvalues, show that family eigenbases symmetric matrices this is generic, strengthening result Monfared Shader. We illustrate constructing new achievable ordered multiplicity lists partial joins graphs providing several families are realizable only two distinct eigenvalues.