Graph

Graph is a mathematical structure used in the field of mathematics and computer science. It is composed of vertices (also known as nodes) and edges (also known as arcs). Each edge connects a pair of vertices. Graphs are used to model many types of relations and processes in physical, biological, social and information systems.

Definition

A graph is a pair G = (V, E), where V is a set of vertices, and E is a set of edges. Each edge is a 2-element subset of V. The two vertices associated with an edge are called the endpoints of the edge.

Types of Graphs

There are several types of graphs, each with its own specific properties and uses. Some of the most common types include:

• Undirected graph - A graph in which edges have no orientation. The edge (x, y) is identical to the edge (y, x).
• Directed graph - A graph in which edges have orientations.
• Weighted graph - A graph in which each edge has a numerical value, known as its weight.
• Bipartite graph - A graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex in the first set to one in the second set.
• Complete graph - A graph in which there is an edge between every pair of vertices.

Applications

Graphs are used in numerous fields, including computer science, physics, biology, social sciences, and network science. They are used to represent networks of communication, data organization, computational devices, the flow of computation, etc.

See Also

• Graph theory
• Graph (discrete mathematics)
• Graph (abstract data type)

References

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