# Complex Network Analytics for Structural-Functional Decoding of Neural Networks
## 1 Introduction  
Deep neural networks have shown unprecedented performance breakthroughs in computer vision, natural language processing, and other fields, but the working mechanism behind their excellent performance has long been regarded as a \"black box\". Traditional research focuses on network parameter optimisation and loss function design, but neglects the fact that neural networks are essentially information processing systems composed of nonlinear computational units connected topologically [1]. Recent studies have shown that the topology of neural networks is profoundly related to their functional properties: the local receptive fields of convolutional layers encode spatial invariance characteristics [2], the cross-layer shortcuts of residual connections guarantee the stability of gradient propagation [3], and the all-connectivity mode of attention mechanism realises global semantic associations [4]. These findings reveal that neural networks are not only collections of parameter values, but also computational graphs with specific topological rules. Understanding the coupling mechanism between network structure and functional performance has become the key to break through the bottleneck of model interpretability and achieve rational design of architectures. Current mainstream model compression methods (e.g., weight pruning, channel trimming) mainly rely on local heuristic criteria such as parameter magnitude or gradient significance. Although such methods can effectively reduce model complexity, they suffer from two fundamental flaws: firstly, evaluation criteria based on single-parameter significance cannot capture synergistic effects among nodes, which may lead to the destruction of key topologies [5]. For example, deleting a certain node with low weight but high median centrality can significantly lengthen the feature transfer path; second, the static pruning strategy ignores the dynamic evolutionary nature of the network structure, and there is a temporal mismatch between the connectivity patterns that are continuously optimised during the training process and the pruning decisions [6]. More seriously, existing methods lack systematic knowledge of the emergent nature of network topology (e.g., small-world properties, modular division of labour), making it difficult for the compressed model to maintain the functional robustness of the original architecture. Complex network theory provides a new paradigm to crack the dilemma. This field has developed tools such as degree distribution analysis, community detection, and percolation models, which are capable of quantitatively characterising the global properties and local patterns of network structures [7]. After mapping neural networks into complex networks, (1) node centrality metrics can identify the key hubs of feature transfer and avoid misdeletion based on parameter magnitude; (2) modularity analysis can locate functionally independent sub-network clusters and guide structural pruning; and (3) dynamic topology tracking can reveal structure-function co-evolutionary laws during the training process. Furthermore, the experiments in this paper demonstrate that the SimpleCNN model based on complex network centrality pruning reduces the accuracy loss by 7.8% when removing 55.5% of parameters compared to the traditional method. In addition, the network topology metrics (e.g., average path length, clustering coefficient) showed significant statistical correlation with the model generalisation error (Pearson r = 0.83, \(p<0.01\)), providing a structural explanation basis for performance prediction. This paper proposes a framework for the study of the structure-function coupling mechanism of neural networks based on complex network analysis. The intrinsic correlation between topological properties and model performance is systematically revealed by establishing a transformation criterion from deep learning models to graph networks.