Applications of Graph Theory in Modern Network Analysis

The modern network architectures, be it the power grids, social media websites or even telecommunication networks, have a very complex network topology that is difficult to analyze using the existing tools. This research paper aims to provide a comprehensive analysis of graph theoretical methods used in modern networks analysis. The paper puts forward a framework that combines classical graph metrics (Wiener Index, Laplacian Energy, Centrality) with graph database techniques and machine learning techniques. With the use of a case study on the European power grid network, it becomes clear how the topological indices, community detection algorithms, and centrality analyses can measure the resilience of the network, critical infrastructure components of the network and price hidden structures in the network. The paper proves that graph theoretical methods have better interpretability and real-time analysis capabilities when compared to relational database methods.