Exploring the mathematical structures used to model pairwise relations between objects.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph is made up of vertices (also called nodes) which are connected by edges (also called links or lines).
Graphs can be used to model many types of relations and processes in physical, biological, social, and information systems. Many practical problems can be represented by graphs and solved using graph algorithms.
There are several types of graphs, including directed graphs (where edges have a direction), undirected graphs (where edges have no direction), weighted graphs (where edges have weights or costs), and many more.
Common graph algorithms include breadth-first search (BFS), depth-first search (DFS), Dijkstra's algorithm for finding shortest paths, and algorithms for detecting cycles, finding minimum spanning trees, and determining connectivity.
Graph theory has applications in computer science, mathematics, engineering, biology, and social sciences. It is used in network analysis, route planning, scheduling, and many other areas.