# Complex Network Analytics for Structural-Functional Decoding of Neural Networks
## 4 Experiment and Result Analysis
### Experimental Analysis
#### 4.2.1 Overall Analysis  
All models contain 618 nodes (corresponding to convolution kernels, fully connected neurons, and pooling units) and 39,936 directed weighted edges (corresponding to connection weights in the parameter matrix). The only difference between the three types of networks is reflected in the distribution of edge weights:  
1. SimpleCNN: edge weights are directly derived from the original parameters of the model. 2. DropoutCNN: the edge weights of the fully connected layer are dynamically imposed with a 0.5 probability mask during training. 3. BatchNormCNN: the convolutional layer edge weights are corrected by batch normalisation scaling. The three network models are identical in the distribution of non-zero element positions of the adjacency matrix, differing only in the values of the weights. This design ensures that subsequent comparative analyses reflect only the effect of the regularisationoperation on the distribution of the weights, rather than changes in network structure. In this paper, we continuously analyse the eigenquantities of the models at each stage of the training process, and the results are shown in Table 2.  
Table 2 systematically compares the network topological features of SimpleCNN, BatchNormCNN, and DropoutCNN to reveal the regularisation mechanism's reshaping law of neural network structure and its guiding significance for model compression. The three experimentally constructed models are identical in terms of the number of nodes, the number of connected edges, the network density, the average clustering coefficient, and the average degree parameter, which verifies the accuracy of the network transformation model--reflecting the effect of different regularisation mechanisms only through the difference in connected edge weights. Crucially, weight normalisation and strength scaling enable cross-architecture comparison by eliminating scale differences caused by BN's weight compression and Dropout's random disconnections. About 10.47% of the activated connections in the network form a moderately sparse architecture, preserving the flexibility of feature transfer while circumventing the computational redundancy of full connections. The analysis of the dynamic parameters of the three networks shows significant divergence: the weight distribution of SimpleCNN exhibits weak activation characteristics (mean 0.0537, variance 0.0064), while the high variance of the strength (0.4114) reflects the characteristic of a few hub nodes to dominate the feature delivery, which increases the vulnerability against attacks while limiting the ability of local feature integration due to zero clustering coefficients. BatchNormCNN achieves enhanced stability of weights through the normalisation mechanism, with the mean value raised to 0.0542 while the variance is compressed by 9.3%, showing its compression effect on extreme weights with enhanced stability of effective connections. In addition, the strength mean value is reduced to 0.013622 and the variance is 0.3729, which balances the information-carrying capacity across nodes, forming a more resilient functional pattern that reduces adversarial vulnerability. In contrast, DropoutCNN exhibits strong regularisation, with the mean value of weights compressed to 0.0222 and the variance sharply reduced by 61%, forcing the network to disperse the feature representation through random inactivation, and homogenising the distribution of node strengths, which significantly improves the adversarial robustness but sacrifices part of the feature transfer efficiency. Dropout concentrates weight distribution via random disconnections, while BatchNorm inverts the distribution through \(\gamma/\beta\) rescaling, forming a bimodal pattern. It is also found that the weight-strength ratios (S/W Ratio) of the three models remain highly consistent (\(64.5\pm 0.1\)), indicating that the neural network spontaneously maintains the conservation of information transfer efficiency per unit weight during training.