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A '''graph''' is a type of visual display that arises in several places in mathematics and [[statistics]].

In mathematics, and especially in topology[[Combinatorics]], a graph is an abstract object consisting of a number of points ("vertices") and lines ("edges") connecting those points, and is used to study networks and similar objects. For example, one could create a graph to represent human friendships: this graph has one point vertex for each person, and an edge between every two people who are friends. According to the theory of six degrees of separation, any two points vertices on this graph are connected by a path that goes along at most six edges! In mathematical terms, a graph is a pair of two sets ''V'' (vertices) and ''E'' (edges), where ''E'' is a subset of Cartesian product <math>V \times V</math>. A graph is "directed" if the pairs are unordered and "undirected" if the pairs are ordered. Edges or vertices of graphs may be assigned additional information Example 1: Vertices are American cities, edges are roads between them, and edges are labeled with the length of the road between cities. A computer given such graph will find the shortest path between any two cities. Example 2: A graph might show correlations and relations between concepts.  [[homosexuality]] [[homosexuality and internalized homophobia|→]] [[internalized homophobia]] [[homosexuality and conservapedia|↓]] [[homosexuality#Homosexuality and Mental Health|↙]] [[conservapedia]] Example 3: A bipartite graph is a graph whose vertices may be divided into two types, presented on left and right. It might show membership.  [[Pope Benedict XVI]] ↘ [[Rick Santorum]] → Catholic [[Mother Teresa]] ↗ [[Mitt Romney]] → Mormon [[Joseph Smith]] ↗ [[Barack Obama]] → President [[Christopher Hitchens]] → Atheist [[Joseph Stalin]] ↗ On the left side there are people, and on the right hand side there are attributes. This bipartite graph models a [[function]]. A planar graph is a graph that can be embedded in the plane (or a sphere) such that there are no crossings between edges. The graphs drawn in examples 2 and 3 are planar, but the graph in example 1 is not, since roads can intersect outside cities.