###### Abstract
Identifying the critical constraints on station throughput capacity, especially under fixed infrastructure conditions, is essential for optimizing station operations and improving network performance. Recent advancements in graph theory and network optimization [41; 42; 43; 44; 45] have provided new tools for modeling railway station operations [46; 47; 48; 49]. Researchers have applied graph-based approaches to model station layouts, throat areas, and interlocking systems, highlighting their utility for route optimization and capacity evaluation [50]. Complex networks, characterized by their intricate relationships and interactions, offer a more nuanced approach to analyzing railway systems. Centrality metrics such as degree centrality, betweenness centrality, and eigenvector centrality, among others [51; 52; 53; 54], are commonly used to evaluate node importance in transportation networks [55; 56; 57]. However, traditional centrality measures often fail to capture the multi-layered, directed nature of railway station networks, where interactions between arrival-departure tracks and throat areas play a crucial role. To address these limitations, recent studies have developed advanced algorithms tailored to railway networks. For instance, [PERSON] et al. [58] proposed a k-shell decomposition-based method to identify critical nodes, while [PERSON] et al. [59] introduced WDKS, a hybrid metric combining degree and k-shell measures with neighborhood influence. Similarly, [PERSON] et al. [60] developed the Curv-PageRank algorithm, integrating curvature with traditional PageRank to assess node importance in complex networks. In railway networks, [PERSON] et al. [57] constructed a dual-layer complex network for China-Europe freight operations, identifying critical nodes using metrics like closeness and betweenness centrality. Their work demonstrates the potential of multi-layered analyses to capture the interdependencies between infrastructure and operations. [PERSON] et al. [61] applied graph neural networks to analyze delay propagation, highlighting the impact of critical nodes on network performance. These studies underscore the versatility of complex network theory in addressing real-world railway challenges. Railway station yard diagrams provide a standardized framework for representing the dependencies among track sections, signals, and routes. These diagrams, consisting of signaling layout and interlocking tables, also called control tables, are essential for modeling railway station networks and ensuring the validity of capacity analysis [62]. By extracting track section sequences from interlocking diagrams, researchers can construct detailed network models to evaluate capacity and identify bottlenecks. Traditional interlocking-based approaches primarily emphasize static infrastructure, often overlooking dynamic factors such as train schedules, route dependencies, and real-time operational constraints. While this study focuses on modeling static infrastructure and interlocking-based connections, the integration of dynamic factors remains a crucial aspect for future research. This study takes an initial step by incorporating network-based importance metrics that indirectly reflect operational constraints, but a fully dynamic representation is beyond the current scope. In this paper, we build upon existing work by introducing multi-layer complex network theory to construct a complex network model of railway station yards. The identification of critical constraints on station design throughput capacity is equivalently transformed into a node importance evaluation problem. We propose node importance evaluation metrics and a comprehensive evaluation method tailored to the characteristics of railway station yards, enabling the effective identification of key nodes. Based on this, we perform case studies on typical stations to validate the proposed method's effectiveness.