Steganography plays a big role in secret communication by concealing secret information in the carrier. This paper presents a graph signal processing-based robust image steganography technique for posting images over social networks. In the embedding, we first obtained a scrambled version of the secret image using quantum scrambling. Next, we applied graph wavelet transformation on both the cover image and scrambled secret image followed by α (alpha) blending on both image signals (cover image signal and scrambled image signal). Finally, inverse graph wavelet transformation of the resulting image was undertaken to obtain the stego image. In this paper, the use of graph wavelet transformation improved interpixel correlation, which resulted in the excellent visual quality of both the stego image and the extracted secret image. Our experiments show that the picture quality of both the cover image and the stego image is exactly the same.