Advances in new electric aerial vehicles have encouraged research on pioneering Urban Air Mobility (UAM) solutions, which would provide fast service for passengers, goods, and emergencies. From this perspective, some air service scenarios have been identified, such as air taxis, airport shuttles, and intercity services. Such air services should be supported by a suitable urban air network, which should comply with several boundary conditions linked to the specific features of this new type of aerial mobility. This paper proposes an Urban Air Network (UAN) model that includes a third (vertical) dimension and whose aim is to satisfy the basic principle of linking origin/destination pairs, as in usual ground transportation networks, by guaranteeing at the same time safe aerial paths between origin/destination pairs with suitable vehicle separations. The proposed UAN consists of multiple 2D graphs on different layers, which allows for the transfer of aerial vehicles in lower airspace. A suitable cost function has been associated with each UAN link in order to compute the shortest paths connecting the origin/destination pairs. The links in a UAN have a dynamic nature and can be enabled or disabled in consideration of capacity issues. In addition, indirect CO2 emissions linked to aerial vehicles (such as operational and disposal phase charges) have been computed to foresee the potential environmental impacts based on the proposed UAN model. The preliminary results of a test case show encouraging results and provide interesting findings for further advancements.