Brain network have been widely used in the study of brain abnormalities in Alzheimer's disease (AD). The construction of network is important for brain characterization and graph neural networks (GNNs)-based classification tasks. Currently, structural magnetic resonance imaging (sMRI)-based structural covariance networks usually only consider interactions between pairs of brain regions at the individual level, and do not take into account higher-order relationships between multiple brain regions or subjects. To overcome these limitations, we proposed the group sparse radiomics representation network (GSR2N) which utilizes group sparse representation (GSR) instead of traditional Pearson correlation (PC) construction method. This reduces inter-individual differences in network topology and accounts for mixing effects among multiple brain regions. We conducted extensive experiments using the ADNI and AIBL dataset on triple graph convolutional network (TGCN) to compare the classification performance of different network construction methods. The results demonstrate that GSR method has the highest classification performance, with intra and inter-dataset test accuracies of 0.894 and 0.856, respectively. This new approach is expected to contribute to future sMRI-based brain network construction and brain disease diagnosis.