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Robust detection of road network in aerial imagery is a challenging task since roads have different pavement texture, road-side surroundings, as well as grades. Roads of different grade have different curvilinear saliency in the aerial imagery. This paper is motivated to incrementally extract roads and construct the topology of the road network of aerial imagery from the higher-grade-first perspective. Inspired by the spanning tree technique, the proposed method starts from the robust extraction of the most salient road segment(s) of the road network, and incrementally connects segments of less saliency of curvilinear structure until all road segments in the network are extracted. The proposed algorithm includes: curvilinear path-based road morphological enhancement, extraction of road segments, and spanning tree search for the incremental road discovery. It is tested on a diverse set of aerial imagery acquired in the city and inter-city areas. Experimental results show that the proposed curvilinear spanning tree (CST) can detect roads efficiently and construct the topology of the road network effectively. It is promising for the change detection of the road network.