Robust and interpretable dementia diagnosis from noisy, non-stationary electroencephalography (EEG) is clinically essential yet remains challenging. To this end, we propose SeeGraph, a Sparse-Explanatory dynamic EEG-graph network that models time-evolving functional connectivity and employs a node-guided sparse edge mask to reveal the connections that drive diagnostic decisions, while remaining robust to noise and cross-site variability. SeeGraph comprises four components: (1) a dual-trajectory temporal encoder that models dynamic EEG with two streams, where node signals capture regional oscillations and edge signals capture interregional coupling; (2) a topology-aware positional encoder that derives graph-spectral Laplacian coordinates from the fused connectivity and augments node embeddings; (3) a node-guided sparse explanatory edge mask that gates the connectivity into a compact subgraph; and (4) a gated graph predictor that operates on the sparsified graph. The framework is trained using cross-entropy loss together with a sparsity regularizer on the mask, yielding noise-robust and interpretable diagnoses. The effectiveness of SeeGraph is validated on public and in-house EEG cohorts, including patients with neurodegenerative dementias and healthy controls, under both raw and noise-perturbed conditions. Its sparse, node-guided explanations highlight disease-relevant connections and align with established clinical findings on functional connectivity alterations, thereby offering transparent cues for neurological evaluation.