Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (or nodes) and edges (or lines). The vertices are the points or locations, and the edges are the connections between them.

Basic Concepts

  • Vertices: The points or nodes in a graph.
  • Edges: The connections between vertices.
  • Degree: The number of edges connected to a vertex.
  • Path: A sequence of vertices connected by edges.
  • Cycle: A path that starts and ends at the same vertex.

Types of Graphs

  • Directed Graph: Edges have a direction.
  • Undirected Graph: Edges have no direction.
  • Weighted Graph: Edges have a weight or value.

Applications

Graph theory has many applications in various fields, including:

  • Computer Science: Network design, algorithms, and data structures.
  • Operations Research: Scheduling, logistics, and optimization.
  • Social Sciences: Network analysis, social networks, and communication.
  • Physics: Network theory, statistical mechanics, and complex systems.

Graph Theory Diagram

For more information on graph theory, you can visit our Graph Theory Tutorial.