Spatial clustering analysis is an important spatial data mining technique. It divides objects into clusters according to their similarities in both location and attribute aspects. It plays an essential role in density distribution identification, hot-spot detection, and trend discovery. Spatial clustering algorithms in the Euclidean space are relatively mature, while those in the network space are less well researched. This study aimed to present a well-known clustering algorithm, named density-based spatial clustering of applications with noise (DBSCAN), to network space and proposed a new clustering algorithm named network space DBSCAN (NS-DBSCAN). Basically, the NS-DBSCAN algorithm used a strategy similar to the DBSCAN algorithm. Furthermore, it provided a new technique for visualizing the density distribution and indicating the intrinsic clustering structure. Tested by the points of interest (POI) in Hanyang district, Wuhan, China, the NS-DBSCAN algorithm was able to accurately detect the high-density regions. The NS-DBSCAN algorithm was compared with the classical hierarchical clustering algorithm and the recently proposed density-based clustering algorithm with network-constraint Delaunay triangulation (NC_DT) in terms of their effectiveness. The hierarchical clustering algorithm was effective only when the cluster number was well specified, otherwise it might separate a natural cluster into several parts. The NC_DT method excessively gathered most objects into a huge cluster. Quantitative evaluation using four indicators, including the silhouette, the R-squared index, the Davis–Bouldin index, and the clustering scheme quality index, indicated that the NS-DBSCAN algorithm was superior to the hierarchical clustering and NC_DT algorithms.