Most hub location studies in the literature use a complete-network structure as an input in developing optimization models. This starting point is not necessarily from assuming that the underlying real-world network (e.g., physical network such as road and rail networks) on which the hub system will operate is complete. It is implicitly or explicitly assumed that a complete-network structure is constructed from the shortest-path lengths between origin-destination pairs on the underlying real-world network through a shortest-path algorithm. Thus, the network structure used as an input in most models is a complete network with the distances satisfying the triangle inequality. Even though this approach has gained acceptance, not using the real-world network and its associated data structure directly in the models may result in several computational and modeling disadvantages. More importantly, there are cases in which the shortest path is not preferred or the triangle inequality is not satisfied. In this regard, we take a new direction and define the p-hub median problem directly on non-complete networks that are representative of many real-world networks. The proposed problem setting and the modeling approach allow several basic assumptions about hub location problems to be relaxed and provides flexibility in modeling several characteristics of real-life hub networks. The proposed models do not require any specific cost and network structure and allow to use the real-world network and its asociated data structure directly. The models can be used with the complete networks as well. We also develop a heuristic based on the proposed modeling aproach and present computational studies. (C) 2018 Elsevier Ltd. All rights reserved.