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Urban black holes and volcanoes are typical traffic anomalies that are useful for optimizing urban planning and maintaining public safety. It is still challenging to detect arbitrarily shaped urban black holes and volcanoes considering the network constraints with less prior knowledge. This study models urban black holes and volcanoes as bivariate spatial clusters and develops a network-constrained bivariate clustering method for detecting statistically significant urban black holes and volcanoes with irregular shapes. First, an edge-expansion strategy is proposed to construct the network-constrained neighborhoods without the time-consuming calculation of the network distance between each pair of objects. Then, a network-constrained spatial scan statistic is constructed to detect urban black holes and volcanoes, and a multidirectional optimization method is developed to identify arbitrarily shaped urban black holes and volcanoes. Finally, the statistical significance of multiscale urban black holes and volcanoes is evaluated using Monte Carlo simulation. The proposed method is compared with three state-of-the-art methods using both simulated data and Beijing taxicab spatial trajectory data. The comparison shows that the proposed method can detect urban black holes and volcanoes more accurately and completely and is useful for detecting spatiotemporal variations of traffic anomalies. [ABSTRACT FROM AUTHOR]