###### Abstract  
Optimizing railway station operations necessitates the identification of critical track sections that constrain design throughput capacity under fixed infrastructure conditions. This paper proposes a novel multi-layer complex network-based approach for modeling and analyzing railway station yard diagrams, reframing the identification of key track sections affecting station throughput capacity as a node importance evaluation problem. In this model, nodes represent track sections included in routes specified by the station interlocking tables, while edges denote sequential connections between nodes. The structural relationships among nodes are captured using adjacency matrix (AM), structural matrix (SM), connection count matrix (CCM), and transition probability matrix (TPM). To evaluate node importance, five key indicators are introduced: connectivity strength (CS), destination node count (DNC), source node count (SNC), node efficiency (NE), and an extended PageRank (EPR). Additionally, a layered network node importance analysis method based on a single indicator, along with a comprehensive evaluation approach for the importance of the multi-layer network node, is presented. A case study conducted on a conventional railway station demonstrates that the proposed method effectively identifies key track sections through both hierarchical single-indicator evaluation and comprehensive assessment approaches. Furthermore, this paper investigates key node evaluation indicators and explores an alternative method based on Principal Component Analysis and Rank Sum Ratio (PCA-RSR), which also proves effective in identifying critical track sections. r 20  
of trains that can traverse a section of track in a given time, though such capacity is rarely achievable. [PERSON] [4] introduced practical and economic perspectives on capacity, while [PERSON] [5] highlighted the influence of section lengths on effective capacity utilization. The UIC 406 methodology [1; 6], widely adopted for capacity analysis, has been refined by researchers to address specific operational contexts, such as single-track lines railways [7], junctions [8], and station yards [9]. Railway capacity analysis methods can be broadly categorized as analytical, simulation-based, and hybrid approaches. Analytical methods, relying on simplified algebraic formulas, provide macroscopic insights into capacity utilization and are particularly suited for strategic and tactical planning [7; 9; 10; 11; 12; 13; 14]. Simulation methods, such as those implemented in RailSys [15], RTC [16; 17], and Open Track [18], offer high precision but require extensive data and computational resources. Hybrid approaches combine analytical simplicity with simulation accuracy, making them increasingly popular for addressing complex railway operations [19]. In addition to these traditional methods, optimization techniques are commonly employed to address sub-problems such as train scheduling, routing, and track allocation [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Despite the utility of these methods, they often require substantial infrastructure, operational, and signaling data, underscoring the need for standardization and systematic modeling. A critical subset of railway capacity is station throughput capacity, which specifically pertains to the maximum number of trains that can traverse a railway station within a given timeframe while ensuring safe and efficient operations. Station throughput capacity is influenced by both infrastructure and operational factors [31; 32]. Infrastructure-related factors, such as track configurations, turnout arrangements, and signaling systems, define the station's design capacity [33; 34; 35]. Operational factors, including scheduling efficiency, management practices, and traffic density, determine dynamic capacity under real-world conditions [33; 36; 37; 38; 39; 40].