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This paper presents a hybrid deep learning framework that combines graph neural networks with convolutional neural networks to predict porous media properties. This approach capitalizes on the capabilities of pre-trained convolutional neural networks to extract ndimensional feature vectors from processed three dimensional micro computed tomography porous media images obtained from seven different sandstone rock samples. Subsequently, two strategies for embedding the computed feature vectors into graphs were explored: extracting a single feature vector per sample (image) and treating each sample as a node in the training graph, and representing each sample as a graph by extracting a fixed number of feature vectors, which form the nodes of each training graph. Various types of graph convolutional layers were examined to evaluate the capabilities and limitations of spectral and spatial approaches. The dataset was divided into 70/20/10 for training, validation, and testing. The models were trained to predict the absolute permeability of porous media. Notably, the proposed architectures further reduce the selected objective loss function to values below 35 mD, with improvements in the coefficient of determination reaching 9%. Moreover, the generalizability of the networks was evaluated by testing their performance on unseen sandstone and carbonate rock samples that were not encountered during training. Finally, a sensitivity analysis is conducted to investigate the influence of various hyperparameters on the performance of the models. The findings highlight the potential of graph neural networks as promising deep learning-based alternatives for characterizing porous media properties. The proposed architectures efficiently predict the permeability, which is more than 500 times faster than that of numerical solvers. [ABSTRACT FROM AUTHOR]