Automatic emotion recognition based on multichannel Electroencephalography (EEG) holds great potential in advancing human-computer interaction. However, several significant challenges persist in existing research on algorithmic emotion recognition. These challenges include the need for a robust model to effectively learn discriminative node attributes over long paths, the exploration of ambiguous topological information in EEG channels and effective frequency bands, and the mapping between intrinsic data qualities and provided labels. To address these challenges, this study introduces the distribution-based uncertainty method to represent spatial dependencies and temporal-spectral relativeness in EEG signals based on Graph Convolutional Network (GCN) architecture that adaptively assigns weights to functional aggregate node features, enabling effective long-path capturing while mitigating over-smoothing phenomena. Moreover, the graph mixup technique is employed to enhance latent connected edges and mitigate noisy label issues. Furthermore, we integrate the uncertainty learning method with deep GCN weights in a one-way learning fashion, termed Connectivity Uncertainty GCN (CU-GCN). We evaluate our approach on two widely used datasets, namely SEED and SEEDIV, for emotion recognition tasks. The experimental results demonstrate the superiority of our methodology over previous methods, yielding positive and significant improvements. Ablation studies confirm the substantial contributions of each component to the overall performance.