The potential of an efficient ride-sharing scheme to significantly reduce traffic congestion, lower emission level, and drivers’ stress, as well as facilitating the introduction of smart cities has been widely demonstrated in recent years. Furthermore, ride sharing can be implemented within a sound economic regime through the involvement of commercial services that creates a win-win for all parties (e.g., Uber, Lyft or Sidecar). This positive thrust however is faced with several delaying factors, one of which is the volatility and unpredictability of the potential benefit (or utilization) of ride-sharing at different times, and in different places. Better understanding of ride-sharing dynamics can help policy makers and urban planners in increase the city’s “ride-sharing friendliness” either by designing new ride-sharing oriented systems, as well as by providing ride-sharing service operators better tools to optimize their services. In this work the following research questions are posed: (a) Is ride-sharing utilization stable over time or does it undergo significant changes? (b) If ride-sharing utilization is dynamic can it be correlated with some traceable features of the traffic? and (c) If ride-sharing utilization is dynamic can it be predicted ahead of time? We analyze a dataset of over 14 million taxi trips taken in New York City. We propose a dynamic travel network approach for modeling and forecasting the potential ride-sharing utilization over time, showing it to be highly volatile. In order to model the utilization's dynamics, we propose a network-centric approach, projecting the aggregated traffic taken from continuous time periods into a feature space comprised of topological features of the network implied by this traffic. This feature space is then used to model the dynamics of ride-sharing utilization over time. The results of our analysis demonstrate the significant volatility of ride-sharing utilization over time, indicating that any policy, design, or plan that would disregard this aspect and chose a static paradigm would undoubtably be either highly inefficient or provide insufficient resources. We show that using our suggested approach it is possible to model the potential utilization of ride sharing based on the topological properties of the rides network. We also show that using this method the potential utilization can be forecasting a few hours ahead of time. One anecdotal derivation of the latter is that perfectly guessing the destination of a New York taxi rider becomes nearly three times easier than rolling a “Snake Eyes” at a casino.