Graph Theory

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.