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We propose flexgrid2vec, a novel approach for image representation learning. Existing visual representation methods suffer from several issues, including the need for highly intensive computation, the risk of losing in-depth structural information and the specificity of the method to certain shapes or objects. flexgrid2vec converts an image to a low-dimensional feature vector. We represent each image with a graph of flexible, unique node locations and edge distances. flexgrid2vec is a multi-channel GCN that learns features of the most representative image patches. We have investigated both spectral and non-spectral implementations of the GCN node-embedding. Specifically, we have implemented flexgrid2vec based on different node-aggregation methods, such as vector summation, concatenation and normalisation with eigenvector centrality. We compare the performance of flexgrid2vec with a set of state-of-the-art visual representation learning models on binary and multi-class image classification tasks. Although we utilise imbalanced, low-size and low-resolution datasets, flexgrid2vec shows stable and outstanding results against well-known base classifiers. flexgrid2vec achieves 96.23% on CIFAR-10, 83.05% on CIFAR-100, 94.50% on STL-10, 98.8% on ASIRRA and 89.69% on the COCO dataset.