Memorization is an essential functionality that enables today's machine learning algorithms to provide a high quality of learning and reasoning for each prediction. Memorization gives algorithms prior knowledge to keep the context and define confidence for their decision. Unfortunately, the existing deep learning algorithms have a weak and nontransparent notion of memorization. Brain-inspired HyperDimensional Computing (HDC) is introduced as a model of human memory. Therefore, it mimics several important functionalities of the brain memory by operating with a vector that is computationally tractable and mathematically rigorous in describing human cognition. In this manuscript, we introduce a brain-inspired system that represents HDC memorization capability over a graph of relations. We propose GrapHD, hyperdimensional memorization that represents graph-based information in high-dimensional space. GrapHD defines an encoding method representing complex graph structure while supporting both weighted and unweighted graphs. Our encoder spreads the information of all nodes and edges across into a full holistic representation so that no component is more responsible for storing any piece of information than another. Then, GrapHD defines several important cognitive functionalities over the encoded memory graph. These operations include memory reconstruction, information retrieval, graph matching, and shortest path. Our extensive evaluation shows that GrapHD: (1) significantly enhances learning capability by giving the notion of short/long term memorization to learning algorithms, (2) enables cognitive computing and reasoning over memorization graph, and (3) enables holographic brain-like computation with substantial robustness to noise and failure.