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Based on graph theory, this paper presents a topological heterogeneity and vulnerability analysis of metro networks where transfer constraint is taken into account. The statistical measurements based on minimal transfer times are defined, such as betweenness, the shortest path and the average transfer times. Based on above, on the one hand, heterogeneity of network is analyzed by adopting entropy theory; on the other hand, travel efficiency and connectivity based on effective paths are proposed to measure the topological vulnerability of metro network. The feasibility and rationality of the methods described above are verified through the Beijing metro network. The results show that the topological analysis neglecting transfer constraint would underestimate the heterogeneity and vulnerability of the metro network: the topological heterogeneity and vulnerability of Beijing metro network with considering transfer constraint are smaller than without considering transfer constraint; in the case of considering transfer constraint, with the scale expansion of network, travel efficiency and convenience increase, and topological heterogeneity and vulnerability of network decrease, but the connectivity of metro network is more vulnerable to node-based attack. • Metro network is abstracted as a model transfers constraint is taken into account. • The statistical measurements based on minimal transfer times are defined, such as betweenness and the shortest path. • Travel efficiency and connectivity based on effective paths are proposed to measure the topological vulnerability of metro network. • The feasibility and rationality of the methods are verified through the Beijing metro network. [ABSTRACT FROM AUTHOR]