TransitiveClosureGraph
gives the transitive closure of the graph g.
TransitiveClosureGraph[{vw,…}]
uses rules vw to specify the graph g.
Details and Options

- TransitiveClosureGraph is also known as reachability graph.
- TransitiveClosureGraph[g] gives a graph with the same vertices as in g, and a vertex u is connected to a vertex v if there is a path from u to v in g.
- TransitiveClosureGraph takes the same options as Graph.
- Possible settings for the Method option include "Warshall", "Warren", and "Purdom". The default setting of Automatic switches among these methods depending on the graph given.
- TransitiveClosureGraph works with undirected graphs, directed graphs, and multigraphs.
Examples
open allclose allBasic Examples (1)
Scope (5)
TransitiveClosureGraph works with undirected graphs:
Use rules to specify the graph:
TransitiveClosureGraph works with large graphs:
Options (3)
Applications (2)
Properties & Relations (6)
The transitive closure graph has the same vertices as the original graph:
An edge uv is in the closure graph if there is a path from u to v in the original graph:
There is a path from 1 to 6 in the given graph, by no direct edge:
There is a direct edge 16 in the transitive closure:
The transitive closure of a connected undirected graph is a complete graph:
Using transitive closure to find the reachability of each vertex in the graph:
TransitiveClosureGraph can be computed using GraphPower:
The transitive closure is the same for a graph and its transitive reduction:
Text
Wolfram Research (2014), TransitiveClosureGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html (updated 2015).
CMS
Wolfram Language. 2014. "TransitiveClosureGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html.
APA
Wolfram Language. (2014). TransitiveClosureGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransitiveClosureGraph.html