Graph (discrete mathematics)

Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.
To avoid ambiguity, this type of object may be called precisely a directed simple graph.
To avoid ambiguity, this type of object may be called precisely a directed multigraph.
Some authors use "oriented graph" to mean the same as "directed graph". Some authors use "oriented graph" to mean any orientation of a given undirected graph or multigraph.
A complete graph is a graph in which each pair of vertices is joined by an edge. A complete graph contains all possible edges.
Most commonly in graph theory it is implied that the graphs discussed are finite. If the graphs are infinite, that is usually specifically stated.
A planar graph is a graph whose vertices and edges can be drawn in a plane such that no two of the edges intersect.
There are several operations that produce new graphs from initial ones, which might be classified into the following categories: