Applied Graph Theory: Techniques and Case Studies from Computational and Scientific Domains

Graph theory is a foundational discipline within mathematics and computer science that studies the properties and structures of graphs, which consist of vertices (nodes) and edges (connections). Beyond its theoretical significance, graph theory serves as a powerful analytical tool for modelling complex systems and relationships in a wide range of real-world applications. This paper provides a comprehensive overview of the practical uses of graph theory across various domains, including computer science, biology, sociology, and transportation systems. By examining how graph-based models are employed to solve problems such as network optimization, biological pathway analysis, and social network mapping, the study underscores the versatility and interdisciplinary relevance of graph theory in addressing contemporary challenges.