## 1 Introduction
applied the centrality indicator to study the ranking of connectivity of three-layer transportation network node cities for air and highway routes along the Belt and Road [16]. However, the above-mentioned scholars are only concerned about a single mode or a combination of two or three transport modes, and there is less research on the integration of railway, air, highway, and water transportation. Additionally, the whole layout of the integrated transportation network has not been formed at the national level, which cannot effectively fit in with the development of the BRI, making it difficult to effectively achieve the orderly linking up of the multi-tiered integrated transportation network consisting of water, land, and air transportation. Hence, this paper addresses the ranking and selection of node cities as the candidate consolidation centers of an integrated transportation network composed of highway, railway, air, and water routes under the BRI to provide a reference for the government in building the consolidation centers. A total of 44 Chinese cities were selected as the candidate consolidation centers under the BRI. Then, the integrated transportation network was formed based on the links of transportation modes among these 44 Chinese cities. It should be noted that the evaluation of consolidation centers in this study was based on the consideration of the above issues of cargo transportation at the national level of China under the BRI. Consequently, each city was viewed as a node in the network without delving into the specific logistic activities within it. Complex network theory has been widely employed in transportation network research in recent years [17; 18]; extensive study has been implemented on single-mode transportation networks, including railway networks [11], subway networks [19; 20], bus networks [21; 22], water networks [23; 24], road networks [25], and air networks [26]. Currently, complex network theory is employed by some scholars to study the single-mode transportation networks under the BRI. [PERSON] et al. used the TOPSIS method combined with complex network theory to select 10 cities from 27 candidate cities as consolidation centers of CR Express [27]. [PERSON] et al. applied the TOPSIS method to select 10 cities from 48 candidate cities of CR Express as consolidation centers using some qualitative indicators [28]. [PERSON] et al. applied the improved TOPSIS method to select the key node of CR Express through multiple centrality evaluation indicators [29]. The entropy weight TOPSIS method was used by [PERSON] et al. [30] to choose eight inner cities as trans-shipment consolidation centers from the regional integration standpoint. Additionally, there are some studies on the impact of consolidation centers. [PERSON] et al. applied agent-based data simulation to verify that the urban consolidation center in Copenhagen can reduce truck mileage by about 65% and emissions by about 70% [31]. On the one hand, there is a lack of studies on the integration of various modes such as air, water, railway, and highway transportation in the aforementioned research. On the other hand, the multi-attribute indicators of transportation networks are rarely considered, which makes it difficult to comprehensively evaluate consolidation centers. Consequently, this study employed complex network theory to integrate various transportation modes--including air, water, highway, and railway--with the aim of constructing an integrated transportation network aligned with the BRI. Using this network, we evaluated the comprehensive scores of candidate node cities as potential consolidation centers. The TOPSIS is a traditional multi-attribute decision-making approach. However, the TOPSIS cannot accurately reflect the similarity of data curves, making it difficult to accurately assess the optimal results.