A *graph* is a collection of objects called *vertices*, *nodes*, or *points*, and connections between them called *edges*.

Graph Theory is the study of graphs.

Graph |
Multigraph |
Pseudograph |
Pseudomultigraph |

In a graph, usually only one connection is allowed between two vertices.

If more than one connection is allowed, the graph is

called a *multigraph*.

Connections from a vertex to itself, called *loops*, are also not usually allowed.

If loops are allowed, the graph is called a *pseudograph*.

If multiple connections *and* loops are allowed, the graph is called a *pseudomultigraph*.

Undirected graph |
Directed graph |
Mixed graph |

Edges usually do not have a direction – they are undordered pairs of vertices.

When edges do have a direction they are called *arcs* or *directed edges*, and the graph is called a *directed graph* or *digraph*.

A graph that has a mixture of directed and undirected edges is called a *mixed graph*.

Unlabelled graph |
Labelled graph |
Weighted graph |

The vertices and edges of a graph may be assigned values or labels.

When the edges are assigned numeric values (such as distances) the graph is called a *weighted graph*.