Traditional approaches to semantic communication tasks rely on the knowledge of the signal-to-noise ratio (SNR) to mitigate channel noise. Moreover, these methods necessitate training under specific SNR conditions, entailing considerable time and computational resources. In this paper, we propose GeNet, a Graph Neural Network (GNN)-based paradigm for semantic communication aimed at combating noise, thereby facilitating Task-Oriented Communication (TOC). We propose a novel approach where we first transform the input data image into graph structures. Then we leverage a GNN-based encoder to extract semantic information from the source data. This extracted semantic information is then transmitted through the channel. At the receiver's end, a GNN-based decoder is utilized to reconstruct the relevant semantic information from the source data for TOC. Through experimental evaluation, we show GeNet's effectiveness in anti-noise TOC while decoupling the SNR dependency. We further evaluate GeNet's performance by varying the number of nodes, revealing its versatility as a new paradigm for semantic communication. Additionally, we show GeNet's robustness to geometric transformations by testing it with different rotation angles, without resorting to data augmentation.