Electroencephalogram (EEG) signals have emerged as a promising biometric modality due to their inherent potential for secure personal identification. However, a persistent challenge in EEG-based biometric systems is the influence of affective state variations, which can compromise the reliability of data acquisition regardless of the protocols employed. Moreover, the non-stationary nature of EEG further exacerbates this issue, as fluctuations in affective states over time can introduce significant variability into the signal. As such, achieving accurate brain fingerprint identification in the presence of affective state changes remains a critical hurdle. This chapter introduces the Multi-scale Convolution and Graph Pooling Network (MCGP), a novel model designed to address these challenges. The MCGP framework employs multiple 1D convolutional layers operating at different scales to dynamically extract and integrate relevant features from EEG signals. Additionally, the model incorporates a graph pooling layer with an attention mechanism, which facilitates the generation of hierarchical graph embeddings. These embeddings are subsequently concatenated and passed through a fully connected classification layer for final identification. Experiments on the SEED and SEED-V datasets show that MCGP achieves an average accuracy of 85.51% on SEED and 88.69% on SEED-V under cross-session conditions with mixed affective states. When a single affective state is maintained across sessions, MCGP reaches 85.75% accuracy on SEED and 88.06% on SEED-V for the same affective state, while achieving 79.57 and 84.52% for different affective states, respectively. These results demonstrate that MCGP effectively mitigates the impact of affective state variations, outperforming baseline methods. Notably, identification performance is slightly better for sessions with the same affective state than for those with different affective states.