  Ride-sharing may substantially contribute to future-compliant sustainable
mobility, both in urban and rural areas. The service quality of ride-sharing
fleets jointly depends on the topology of the underlying street networks, the
spatio-temporal demand distributions, and the dispatching algorithms. Yet,
efficiency of ride-sharing services is typically quantified by economic or
ecological ad-hoc measures that do not transfer to new service regions with
different characteristics. Here we derive a generic measure of ride-sharing
efficiency based on the intrinsic ride-sharing dynamics that follows a
universal scaling law across network topologies. We demonstrate that the same
scaling holds across street networks of distinct topologies, including cities,
islands and rural areas, and is insensitive to modifying request distributions
and dispatching criteria. These results further our understanding of the
collective dynamics of ride-sharing fleets and may enable quantitative
evaluation of conditions towards increasing the feasibility of creating or
transferring ride-sharing services to previously unserviced regions.
