Hip osteoarthritis (HOA) is a degenerative joint disease that leads to the progressive destruction of subchondral bone and cartilage at the hip joint. Development of effective treatments for HOA remains an open problem, primarily due to the lack of knowledge of its pathogenesis and a typically late-stage diagnosis. We describe a novel network analysis methodology for micro-computed tomography (micro-CT) images of human trabecular bone. We explored differences between the trabecular bone microstructure of femoral heads with and without HOA. Large-scale automated extraction of the network formed by trabecular bone revealed significant network properties not previously reported for bone. Profound differences were discovered, particularly in the proximal third of the femoral head, where HOA networks demonstrated elevated numbers of edges, vertices and graph components. When further differentiating healthy joint and HOA networks, the latter showed fewer small-world network properties, due to decreased clustering coefficient and increased characteristic path length. Furthermore, we found that HOA networks had reduced length of edges, indicating the formation of compressed trabecular structures. In order to assess our network approach, we developed a deep learning model for classifying HOA and control cases, and we fed it with two separate inputs: (i) micro-CT images of the trabecular bone, and (ii) the network extracted from them. The model with plain micro-CT images achieves 74.63% overall accuracy while the trained model with extracted networks attains 96.47% accuracy. We anticipate our findings to be a starting point for a novel description of bone microstructure in HOA, by considering the phenomenon from a graph theory viewpoint.