Despite the promising performance of state of the art approaches for Parkinsons Disease (PD) detection, these approaches often analyze individual speech segments in isolation, which can lead to suboptimal results. Dysarthric cues that characterize speech impairments from PD patients are expected to be related across segments from different speakers. Isolated segment analysis fails to exploit these inter segment relationships. Additionally, not all speech segments from PD patients exhibit clear dysarthric symptoms, introducing label noise that can negatively affect the performance and generalizability of current approaches. To address these challenges, we propose a novel PD detection framework utilizing Graph Convolutional Networks (GCNs). By representing speech segments as nodes and capturing the similarity between segments through edges, our GCN model facilitates the aggregation of dysarthric cues across the graph, effectively exploiting segment relationships and mitigating the impact of label noise. Experimental results demonstrate theadvantages of the proposed GCN model for PD detection and provide insights into its underlying mechanisms