View source for Graph (mathematics)

In [[mathematics]], and more specifically in [[Graph (mathematics)|graph theory]], a '''graph''' is a representation of a set of objects where some pairs of [[Object mathematics)|objects]] are connected by [[Link (geometry)|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]]

== External links == 

* [https://en.wikipedia.org/wiki/Graph_(mathematics) Graph (mathematics)] @ Wikipedia