## Multiple Line Charts: Performance Comparison of Graph Neural Networks ### Overview The image presents five line charts comparing the performance of different graph neural network (GNN) models across varying privacy budgets. Each chart corresponds to a different dataset: Bitcoin_Alpha, Bitcoin_OCT, WikiRfA, Slashdot, and Epinions. The performance metric is the Area Under the Curve (AUC), plotted against the privacy budget (epsilon). The GNN models compared are SDGNN, SiGAT, SGCN, GAP, LSNE, and ASGL (Proposed). ### Components/Axes * **Title:** Performance Comparison of Graph Neural Networks across different datasets. * **X-axis:** Privacy budget (epsilon). Scale: 1 to 6 in integer increments. * **Y-axis:** AUC (Area Under the Curve). Scale: 0.50 to 0.90 in increments of 0.05. * **Legend:** Located at the top of the image. * SDGNN: Gray line with circle markers. * SiGAT: Pink line with circle markers. * SGCN: Blue line with circle markers. * GAP: Green line with square markers. * LSNE: Yellow line with diamond markers. * ASGL (Proposed): Red line with triangle markers. * **Chart Titles:** * (a) Bitcoin\_Alpha * (b) Bitcoin\_OCT * (c) WikiRfA * (d) Slashdot * (e) Epinions ### Detailed Analysis #### (a) Bitcoin\_Alpha * **SDGNN (Gray):** Starts at approximately 0.68 AUC at privacy budget 1, gradually increases to approximately 0.78 at privacy budget 6. * **SiGAT (Pink):** Starts at approximately 0.72 AUC at privacy budget 1, gradually increases to approximately 0.80 at privacy budget 6. * **SGCN (Blue):** Starts at approximately 0.52 AUC at privacy budget 1, increases to approximately 0.75 at privacy budget 6. * **GAP (Green):** Starts at approximately 0.57 AUC at privacy budget 1, gradually increases to approximately 0.75 at privacy budget 6. * **LSNE (Yellow):** Starts at approximately 0.51 AUC at privacy budget 1, gradually increases to approximately 0.75 at privacy budget 6. * **ASGL (Proposed) (Red):** Starts at approximately 0.77 AUC at privacy budget 1, increases to approximately 0.86 at privacy budget 6. #### (b) Bitcoin\_OCT * **SDGNN (Gray):** Starts at approximately 0.78 AUC at privacy budget 1, gradually increases to approximately 0.82 at privacy budget 6. * **SiGAT (Pink):** Starts at approximately 0.75 AUC at privacy budget 1, gradually increases to approximately 0.88 at privacy budget 6. * **SGCN (Blue):** Starts at approximately 0.57 AUC at privacy budget 1, increases to approximately 0.77 at privacy budget 6. * **GAP (Green):** Starts at approximately 0.56 AUC at privacy budget 1, gradually increases to approximately 0.68 at privacy budget 6. * **LSNE (Yellow):** Starts at approximately 0.52 AUC at privacy budget 1, gradually increases to approximately 0.86 at privacy budget 6. * **ASGL (Proposed) (Red):** Starts at approximately 0.80 AUC at privacy budget 1, increases to approximately 0.88 at privacy budget 6. #### (c) WikiRfA * **SDGNN (Gray):** Starts at approximately 0.72 AUC at privacy budget 1, gradually increases to approximately 0.82 at privacy budget 6. * **SiGAT (Pink):** Starts at approximately 0.75 AUC at privacy budget 1, gradually increases to approximately 0.85 at privacy budget 6. * **SGCN (Blue):** Starts at approximately 0.68 AUC at privacy budget 1, increases to approximately 0.85 at privacy budget 6. * **GAP (Green):** Starts at approximately 0.55 AUC at privacy budget 1, gradually increases to approximately 0.60 at privacy budget 6. * **LSNE (Yellow):** Starts at approximately 0.68 AUC at privacy budget 1, gradually increases to approximately 0.80 at privacy budget 6. * **ASGL (Proposed) (Red):** Starts at approximately 0.78 AUC at privacy budget 1, increases to approximately 0.85 at privacy budget 6. #### (d) Slashdot * **SDGNN (Gray):** Starts at approximately 0.60 AUC at privacy budget 1, gradually increases to approximately 0.80 at privacy budget 6. * **SiGAT (Pink):** Starts at approximately 0.78 AUC at privacy budget 1, gradually increases to approximately 0.88 at privacy budget 6. * **SGCN (Blue):** Starts at approximately 0.60 AUC at privacy budget 1, increases to approximately 0.78 at privacy budget 6. * **GAP (Green):** Starts at approximately 0.60 AUC at privacy budget 1, gradually increases to approximately 0.72 at privacy budget 6. * **LSNE (Yellow):** Starts at approximately 0.68 AUC at privacy budget 1, gradually increases to approximately 0.82 at privacy budget 6. * **ASGL (Proposed) (Red):** Starts at approximately 0.70 AUC at privacy budget 1, increases to approximately 0.88 at privacy budget 6. #### (e) Epinions * **SDGNN (Gray):** Starts at approximately 0.68 AUC at privacy budget 1, gradually increases to approximately 0.82 at privacy budget 6. * **SiGAT (Pink):** Starts at approximately 0.68 AUC at privacy budget 1, gradually increases to approximately 0.88 at privacy budget 6. * **SGCN (Blue):** Starts at approximately 0.58 AUC at privacy budget 1, increases to approximately 0.82 at privacy budget 6. * **GAP (Green):** Starts at approximately 0.58 AUC at privacy budget 1, gradually increases to approximately 0.72 at privacy budget 6. * **LSNE (Yellow):** Starts at approximately 0.70 AUC at privacy budget 1, gradually increases to approximately 0.80 at privacy budget 6. * **ASGL (Proposed) (Red):** Starts at approximately 0.72 AUC at privacy budget 1, increases to approximately 0.88 at privacy budget 6. ### Key Observations * **ASGL (Proposed)** generally performs well across all datasets, often achieving the highest AUC values. * **GAP** consistently shows the lowest performance among the compared models. * The performance of all models generally improves as the privacy budget (epsilon) increases. * The relative performance of the models varies across different datasets. ### Interpretation The charts demonstrate the trade-off between privacy and utility (performance) in graph neural networks. As the privacy budget (epsilon) increases, the models generally achieve higher AUC scores, indicating better performance. However, higher epsilon values also imply weaker privacy guarantees. The ASGL (Proposed) model appears to strike a good balance between privacy and utility, consistently achieving high AUC scores across different datasets. The GAP model, on the other hand, consistently underperforms compared to the other models. The choice of the best model depends on the specific dataset and the desired trade-off between privacy and performance.