In recent years, tasks of machine learning ranging from image processing & audio/video analysis to natural language understanding have been transformed by deep learning. The data content in all these scenarios are expressed via Euclidean space. However, a considerable amount of application data is structured in non-Euclidean space and is expressed as graphs, e.g. dealing with complicated interactions & object interdependencies. Modelling physical systems, learning molecular signatures, identifying protein interactions and predicting diseases involve utilising a model that can adapt from graph data. Graph neural networks (GNNs), specified as artificial-neural models, employ message transmission between graph nodes to represent graph dependencies and are primarily used in the non-Euclidean domain. Variants of GNN like Graph Recurrent Networks (GRN), Graph Auto Encoder (GAE), Graph Convolution Networks (GCN), Graph Adversarial Methods & Graph Reinforcement learning have exhibited breakthrough productivity on a wide range of tasks, especially in the field of bioinformatics, in recent years as a result of the rapid collection of biological network data. Apart from presenting all existing GNN models, mathematical analysis and comparison of the variants of all types of GNN have been highlighted in this survey. Graph neural networks are investigated for their potential real-world applications in various fields, focusing on Bioinformatics. Furthermore, resources for evaluating graph neural network models and accessing open-source code & benchmark data sets are included. Ultimately, we provide some (seven) proposals for future research in this rapidly evolving domain. GNNs have the potential to be an excellent tool for solving a wide range of biological challenges in bioinformatics research, as they are best represented as connected complex graphs., Comment: 39 pages, 13 figures, 21 tables