Difference between revisions of "Graph (mathematics)"

Revision as of 05:27, 1 September 2015

In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of objects are connected by links.

Description

The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges.

Vertices are also called nodes or points, and edges are also called arcs or lines.

Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.

Undirected graphs

If the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A.

Directed graphs

If there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowledge of someone is not necessarily a symmetric relation (that is, one person knowing another person does not necessarily imply the reverse; for example, many fans may know of a celebrity, but the celebrity is unlikely to know of all their fans).

This type of graph is called a directed graph and the edges are called directed edges or arcs.

History

The word "graph" was first used in this sense by J.J. Sylvester in 1878.

See also

• Graph theory
• Link (geometry)
• Mathematics
• Symmetric relation

External links

• Graph (mathematics) @ Wikipedia