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Graph theory is the study of graphs, which are mathematical structures used to model pairwise relationships between objects. A graph consists of vertices or nodes connected by edges. These concepts are fundamental in mathematics and computer science, with applications ranging from social network analysis to circuit design. In the context of combinatorics, a branch of discrete mathematics, graph theory investigates the properties of graphs and the algorithms for their manipulation. It involves analyzing the structure of graphs and understanding how different components interact with each other. This field is deeply intertwined with various areas of science and mathematics, making it a natural fit under combinatorics within the broader categories of mathematics and science.