In the
mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
field of
graph theory
In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
, graph operations are
operations
Operation or Operations may refer to:
Arts, entertainment and media
* ''Operation'' (game), a battery-operated board game that challenges dexterity
* Operation (music), a term used in musical set theory
* ''Operations'' (magazine), Multi-Man ...
which produce new
graphs from initial ones. They include both
unary (one input) and
binary (two input) operations.
Unary operations
Unary operations create a new graph from a single initial graph.
Elementary operations
Elementary operations or editing operations, which are also known as graph edit operations, create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices,
edge contraction, etc.
The
graph edit distance between a pair of graphs is the minimum number of elementary operations required to transform one graph into the other.
Advanced operations
Advanced operations create a new graph from initial one by a complex changes, such as:
*
transpose graph
In the mathematical and algorithmic study of graph theory, the converse, transpose or reverse, entry 2.24 of a directed graph is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of ...
;
*
complement graph;
*
line graph;
*
graph minor;
*
graph rewriting;
*
power of graph;
*
dual graph;
*
medial graph;
*