Graph classification, aimed at capturing the characteristics of the entire graph, has become an important research hotspot in numerous tasks. The mainstream models currently in use mostly employ Graph Neural Networks (GNNs) as processing tools. However, GNN models have a high computational complexity when dealing with large-scale graph data. Moreover, they are quite sensitive to changes in graph structures, making it difficult to maintain stable performance in dynamic graph environments. At the same time, in multi-label classification tasks, they face the issue of ambiguity in node features and topological structures. To address these challenges, our solution integrates two collaborative components: 1) a Mamba module that combines GAT to learn the features of the network from node connections and node features; 2) a network analysis module that utilizes the Kolmogorov-Arnold Network (KAN) to decode the structural patterns within the network and the specific variations among different networks. Comprehensive evaluations on four benchmark datasets have revealed the outstanding performance of EMK-GC, surpassing the state-of-the-art baselines with an increase of 6.49% in AUC and 6.60% in accuracy, while also demonstrating enhanced robustness on different networks.