Graph signal processing (GSP) is becoming a major tool in biomedical signal and image analysis. In most GSP techniques, graph structures and edge weights have been typically set via statistical and computational methods. More recently, graph structure learning methods offered more reliable and flexible data representations. In this work, we introduce a graph learning approach for melanoma detection in dermoscopic images based on two graph-theoretic representations: superpixel ensemble graphs (SEG) and superpixel hierarchy graphs (SHG). For these two types of graphs, superpixel maps of a skin lesion image are respectively generated at multiple levels without and with parentchild constraints among superpixels at adjacent levels, where each level corresponds to a subgraph with a different number of nodes (20, 40, 60, 80, or 100 nodes). Two edge weight assignment techniques are explored: handcrafted Gaussian weights and learned weights based on optimization methods. The graph nodal signals are assigned based on texture, geometric, and color superpixel features. In addition, the effect of graph edge thresholding is investigated by applying different thresholds (25%, 50%, and 75%) to prune the weakest edges and analyze the impact of pruning on the melanoma detection performance. Experimental evaluation of the proposed method is performed with different classifiers trained and tested on the publicly available ISIC2017 dataset. Data augmentation is applied to alleviate class imbalance by adding more melanoma images from the ISIC archive. The results show that learned superpixel ensemble graphs with textural nodal signals give the highest performance reaching an accuracy of 99.00% and an AUC of 99.59%.