Transpose graph
Encyclopedia
In the mathematical and algorithmic study of graph theory
, the converse, transpose or reverse of a directed graph
G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u,v) then the converse/transpose/reverse of G contains an edge (v,u) and vice versa.
The name "converse" arises because the reversal of arrows corresponds to taking the converse
of an implication in logic.
The name "transpose" is because the adjacency matrix
of the transposed directed graph is the transpose
of the adjacency matrix of the original directed graph.
The name "reverse" is obvious.
There is no general agreement on preferred terminology.
The converse is denoted symbolically as G, GT, GR, or other notations, depending on which terminology is used and which book or article is the source for the notation.
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, the converse, transpose or reverse of a directed graph
Directed graph
A directed graph or digraph is a pair G= of:* a set V, whose elements are called vertices or nodes,...
G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u,v) then the converse/transpose/reverse of G contains an edge (v,u) and vice versa.
The name "converse" arises because the reversal of arrows corresponds to taking the converse
Converse
Converse is an American shoe company that has been making shoes, lifestyle fashion and athletic apparel since the early 20th century. Converse is one of the earliest pioneers in the sneaker and sporting good industry founded in 1908.- 1908–1941: Early days :...
of an implication in logic.
The name "transpose" is because the adjacency matrix
Adjacency matrix
In mathematics and computer science, an adjacency matrix is a means of representing which vertices of a graph are adjacent to which other vertices...
of the transposed directed graph is the transpose
Transpose
In linear algebra, the transpose of a matrix A is another matrix AT created by any one of the following equivalent actions:...
of the adjacency matrix of the original directed graph.
The name "reverse" is obvious.
There is no general agreement on preferred terminology.
The converse is denoted symbolically as G, GT, GR, or other notations, depending on which terminology is used and which book or article is the source for the notation.