We propose a new graph-based method for exploration and representative set selection in vector spaces for classification tasks, and demonstrate the results on a well-known MNIST dataset. Our method reveals significant variations in the similarity structure among vectors corresponding to different label classes. To better capture these differences, we construct similarity-based graphs (networks) with a balanced number of edges within each label class, rather than using a single similarity cutoff across all classes. This tailored approach provides deeper insights into class-specific similarities. We further analyze the resulting graphs by computing various global and local structural properties. Additionally, we introduce a representative set selection model based on independent and dominating sets. We validate the effectiveness of our approach by training a Convolutional Neural Network (CNN) on these representative sets and comparing performance against randomly selected sets of images of the same size.