The connectivity of the urban public transport network and the convenience of transfers between modes of transit are important factors that affect whether passengers choose public transport. Identifying the key nodes that affect network connectivity, direct access, transfers, and clarifying the main factors that restrict the network efficiency play important roles in improving the efficiency of the public transport network and establishing a “green city”. On this premise, this paper constructs two single-layer networks and a composite network that can reflect the transfer relationship between ‘bus–bus’, ‘metro–metro’, and ‘metro–bus’ based on the method of Space-P. The composite network realizes the integration study of homogeneous and heterogeneous stops, lines, and transfer relationships in the public transport network. At the same time, five kinds of centrality indexes are applied to the transport transfer network, and the significance of these indexes in the network is explained. Through the comprehensive analysis of these five types of indexes, the key nodes affecting the network connectivity, direct access and transfer efficiency, can be identified more accurately. Taking the public transport network of Xi’an as an example, the structural characteristics of the networks, including scale-free and small-world characteristics, were empirically analyzed. The main stops that play important roles in networks were identified based on the integrated centrality, degrees, and weight degrees. The research results showed the following: (1) Xi’an’s metro network, bus network, and metro–bus composite network all have scale-free and small-world characteristics. (2) The influence of the key stops of the metro network is concentrated, while the influence of the key stops of the bus network is scattered. (3) The public transport network in the first ring road area of Xi’an has the highest degree of direct access, and the core areas of the south, west, and north of Xi’an also have high direct access. However, the direct access in the area east of Xi’an is slightly lower. (4) Xi’an’s bus transport network covers a large area, showing the characteristics of a dual-core “central + southern” network. (5) The metro–bus composite network demonstrates a closer connection between stops and a more balanced network. (6) Finally, the degree of direct access to stops in the bus transport network and metro transport network shows the characteristics of “the single core is dominant, and the circle diffusion weakens step by step”.