Biometric systems represent valid solutions in tasks like user authentication and verification. However, especially when physical biometrics are used, as is the case of iris recognition, they require specific hardware such as retina scanners, sensors, or HD cameras to achieve relevant results. In this sense, the majority of the prior studies propose to improve the acquisitions of long-range (LR) iris images using specific technologies, without trying to analyze their potential during the processing and classification phase. For this reason, in this work, we propose a novel approach that uses LR distance images taken from traditional cameras for implementing an iris verification system. More specifically, we present a novel methodology for converting LR iris images into graphs based on 1) converting the image in greyscale, 2) discretizing it and 3) performing a binarization, then, 4) graph nodes are defined by detecting the connected components in the binarized image, as well as their 5) features and 6) their edges. Once these graphs are extracted, they are used as input in Graph Siamese Neural Networks (GSNN) to predict whether two graphs belong to the same person. In this study, three experiments are carried out. In the first one, we evaluate how the number of nodes in the generated graphs affects the verification system. In the second one, specific filters are used to enhance the spectral information of the LR images, changing their graph definition. Finally, in the third one, we evaluate how the number of users impacts the verification system performance.Results show that a small number of nodes or using too many nodes worsens the model performance, whereas it is possible to improve the F1-score of the GSNN using spectral enhanced images (up to 77%). Furthermore, increasing the number of users shows a small deterioration in the GSNNs performance. These results demonstrate the suitability of this approach, encouraging the community to explore the usage of traditional LR distance images and graph application in biometric systems. CCS Concepts: • Theory of computation → Graph algorithms analysis; • Security and privacy → Biometrics; • Computing methodologies → Spectral methods; Image processing.