Graph Embedding (GE) along with its linearization outperforms the traditional linear dimension reduction techniques in face recognition, but there is still room for improvement on GE. This paper proposes an eigenvector weighting technique for a realization of linear GE, namely Neighbourhood Preserving Embedding (NPE) in face verification. The proposed method is called Eigenvector Weighting Function - NPE (EWF-NPE). The eigenspace is decomposed into three subspaces: (1) a subspace that is attributed to facial intra-class variations, (2) a subspace comprises of intrinsic facial characteristics, and (3) a subspace that is attributed to sensor and other external noises. Eigenfeatures are weighted differently in these subspaces. The proposed EWF-NPE ensures that only stable face subspace which yields informative data is emphasized, while the other two noise subspaces are deemphasized. Experimental investigations on FRGC and FERET databases demonstrate promising results of the proposed method.