Ride-hailing platforms have a profound impact on urban transportation systems, and their performance largely depends on how intelligently they dispatch vehicles in real time. In this work, we develop a new approach to online vehicle dispatch that strengthens a platform's ability to serve more requests under demand uncertainty. We introduce a novel measure called sink proximity, a network-science-inspired measure that captures how demand and vehicle flows are likely to evolve across the city. By integrating this measure into a shareability-network framework, we design an online dispatch...