We propose a domain adaptation algorithm that relies on a graph representation of data samples in the source and target domains. The algorithm combines the information of the known class labels in the source and target domains through the Fourier coefficients of the class label function in the two graphs. The proposed method does not require an ordering or a one-to-one mapping between the samples of the source and target domains; instead, it uses only a small set of matched pairs that serve the purpose of "aligning" the source and target Fourier bases. The estimation of the coefficients of the label function in the source and target Fourier bases is then formulated as a simple convex optimization problem. The proposed domain adaptation algorithm is tested in face recognition under varying pose and illumination and is observed to provide significant improvement over reference classification approaches especially when the data distributions in the source and target domains differ significantly.