In recent years, Geo-Indistinguishability (GeoI) has been increasingly explored for protecting location privacy in location-based services (LBSs). GeoI is considered a theoretically rigorous location privacy notion since it extends differential privacy to the setting of location privacy. However, GeoI does not consider the road network, which may cause insufficiencies in terms of both privacy and utility for LBSs over a road network. In this paper, we first empirically evaluate the privacy guarantee and the utility loss of GeoI for LBSs over road networks. We identify an extra privacy loss when adversaries have the knowledge of road networks and the degradation of LBS quality of service. Second, we propose a new privacy notion, Geo-Graph-Indistinguishability (GeoGI), for protecting location privacy for LBSs over a road network and design a Graph-Exponential mechanism (GEM) satisfying GeoGI. We also show the relationship between GeoI and GeoGI to explain theoretically why GeoGI is a more suitable privacy notion over road networks. Finally, we evaluate the empirical privacy and utility of the proposed mechanism in real-world road networks. Our experiments confirm that GEM achieves higher utility for LBSs over a road network than the planar Laplace mechanism for GeoI under the same empirical privacy level.