This article embarks on an insightful journey through the realm of advanced data analysis techniques which can be used in the insurance area, with a keen focus on the applications and capabilities of Graph Neural Networks (GNN) in the following sector. The article is structured into several chapters, which include the overview of existing and commonly used approaches of the data representation, the possible ways of data analysis of the data in such a representation, deep dive into the concept of GNN for the graph data analysis and the applicability of each approach in the insurance industry. The initial chapter introduces the two main concepts of the data representation, which are the commonly used relational database and the more modern approach of dimensional data design. Then the focus is moved to the graph data representation, which also can be used for data analysis in the cloud environment. To achieve the best applicability in the insurance industry, particularly in underwriting and claims management, the article analyzes the advantages of each approach to the data representation as well as its drawbacks. To conclude the chapter, the comparison table of the three approaches is presented. Based on the comparison table, the decision to use the graph representation is made as it enables the industry to unravel complex relationships and dependencies amid various data points—such as policyholder history, incident particulars, and third-party information—resulting in more accurate risk assessments and efficient claim resolutions. Then the article presents the concept of Graph Neural Networks, a rather new concept which can be used to analyze the data, represented in a graph form using machine learning algorithms. The potential of using this approach for the data analysis in the insurance area and some possible use cases are described. The advantages of using this approach include ability to effectively capture and leverage the complex relationships inherent in graph- structured data and a powerful framework for analyzing and processing graph-structured data. However, the potential drawbacks of the approach such as complexity to design and difficulties in scaling are also considered. Further along, the article probes the strategic integration of Graph Neural Networks with real-time and dynamic data environments, examining their adaptability to evolving network patterns and temporal dependencies. We discuss how this adaptability is paramount in contexts like real-time decision-making and predictive analysis, which are crucial for staying agile in a rapidly changing market landscape. Then the exact use cases of the GNN applicability in the insurance area are provided, including the claim assignment and underwriting process are described in detail. Furthermore, the simplified mathematical formulation of the underwriting process is provided, which elaborates the role GNNs play in propelling actuarial science with their capability to incorporate node attributes, edge information, and graph structure into a composite risk assessment algorithm. The article concludes by describing that with the new technologies, the graph representation may become the new standard for the data analysis in the cloud environment, especially for the insurance area, stressing the pivotal role of GNNs in navigating the complexities of interconnected, dynamic data and advocating for their continued research and development to unlock even greater potentials across various sectors.