Graphs consist vertices edges from "summary" of Introduction to Graph Theory by Douglas Brent West
A graph is a mathematical structure that consists of two main components: vertices and edges. Vertices are the points or nodes in a graph, while edges are the connections between these points. In other words, a graph is a collection of points joined by lines. Vertices are typically represented by circles or dots, while edges are represented by lines or arcs connecting these points. Vertices can be thought of as the entities in a graph, such as cities in a map, while edges represent the relationships or connections between these entities, such as roads connecting the cities. In a graph, each edge connects two vertices, and these vertices are said to be adjacent to each other. The number of vertices connected by an edge is known as the degree of that edge. For example, a graph with three vertices connected by two edges would have a total degree of four (2 + 2). The concept of vertices and edges is fundamental to graph theory, as it allows mathematicians to study and analyze the relationships between different entities. By representing these relationships as vertices and edges, graph theory provides a powerful tool for solving a wide range of real-world problems. In summary, graphs consist of vertices, which represent the entities in a graph, and edges, which represent the connections between these entities. By studying the relationships between vertices and edges, mathematicians can gain valuable insights into various systems and structures.
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