Graph theory and network models

Graph theory is a fundamental area of discrete mathematics that studies structures formed by vertices and edges, providing powerful tools for modeling pairwise relationships. Network models, built upon graph-theoretic principles, are widely used to represent and analyze real-world systems such as communication networks, transportation systems, social networks, biological interactions, and information flow. This chapter introduces the foundations of graph theory, key concepts and types of graphs, classical graph algorithms, and major network models. Emphasis is placed on the practical relevance of graph theory m modeling, analyzing, and optimizing complex networks across disciplines.