Self-supervised learning and pre-training strategieshave developed over the last few years especiallyfor Convolutional Neural Networks (CNNs). Re-cently application of such methods can also be no-ticed for Graph Neural Networks (GNNs) . In thispaper, we have used a graph based self-supervisedlearning strategy with different loss functions (Bar-low Twins[Zbontaret al., 2021], HSIC[Tsaiet al.,2021], VICReg[Bardeset al., 2021]) which haveshown promising results when applied with CNNspreviously. We have also proposed a hybrid lossfunction combining the advantages of VICReg andHSIC and called it as VICRegHSIC. The perfor-mance of these aforementioned methods have beencompared when applied to 7 different datasets suchas MUTAG, PROTEINS, IMDB-Binary, etc. Ex-periments showed that our hybrid loss function per-formed better than the remaining ones in 4 out of7 cases. Moreover, the impact of different batchsizes, projector dimensions and data augmentationstrategies have also been explored.