Reachability Matrix - Revision history

Laouris at 12:56, 9 January 2022

2022-01-09T12:56:23Z

← Older revision		Revision as of 12:56, 9 January 2022
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	A vertex ''s'' can reach a vertex ''t'' (and ''t'' is reachable from ''s'') if there exists a sequence of adjacent vertices (i.e. a walk) which starts with ''s'' and ends with ''t''.		A vertex ''s'' can reach a vertex ''t'' (and ''t'' is reachable from ''s'') if there exists a sequence of adjacent vertices (i.e. a walk) which starts with ''s'' and ends with ''t''.

	The '''Reachability Matrix''' can be derived from the [[Adjacency Matrix]] if the ~~remations~~ transitive ~~multi-level~~		The '''Reachability Matrix''' can be derived from the [[Adjacency Matrix]] if the relation modeled is [[transitive]] and [[multilevel]].

	Usually there are several Adjacency matrices that have the same Reachability Matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the ~~reachability matrix~~.		Usually, there are several Adjacency matrices that have the same Reachability Matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the Reachability Matrix.

Laouris at 12:54, 9 January 2022

2022-01-09T12:54:36Z

← Older revision		Revision as of 12:54, 9 January 2022
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	In graph theory, reachability refers to the ability to get from one vertex to another within a graph.		In graph theory, '''''reachability''''' refers to the ability to get from one [[Vertex\|vertex]] to another within a graph.

	A vertex s can reach a vertex t (and t is reachable from s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with s and ends with t.		A vertex ''s'' can reach a vertex ''t'' (and ''t'' is reachable from ''s'') if there exists a sequence of adjacent vertices (i.e. a walk) which starts with ''s'' and ends with ''t''.

	The Reachability Matrix can be derived from the Adjacency ~~matrix~~ if transitive multi-level		The '''Reachability Matrix''' can be derived from the [[Adjacency Matrix]] if the remations transitive multi-level

	Usually there are several Adjacency matrices that have the same Reachability Matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the reachability matrix.		Usually there are several Adjacency matrices that have the same Reachability Matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the reachability matrix.

Laouris at 11:32, 9 January 2022

2022-01-09T11:32:12Z

← Older revision		Revision as of 11:32, 9 January 2022
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	In graph theory, reachability refers to the ability to get from one vertex to another within a graph~~. A vertex~~		In graph theory, reachability refers to the ability to get from one vertex to another within a graph.
	s
	~~s can reach a vertex~~
	t
	~~t (and~~
	t
	~~t is reachable from~~
	s
	~~s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with~~
	s
	~~s and ends with~~
	t
	t.

	Usually there are several ~~adjacency~~ matrices that have the same ~~reachability matrix~~. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the reachability matrix.		A vertex s can reach a vertex t (and t is reachable from s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with s and ends with t.

			The Reachability Matrix can be derived from the Adjacency matrix if transitive multi-level

			Usually there are several Adjacency matrices that have the same Reachability Matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the reachability matrix.

Laouris: Created page with "In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s s can reach a vertex t t (and t t is reachable from s s) i..."

2022-01-09T11:30:12Z

Created page with "In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s s can reach a vertex t t (and t t is reachable from s s) i..."

New page

In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex
s
s can reach a vertex
t
t (and
t
t is reachable from
s
s) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with
s
s and ends with
t
t.

Usually there are several adjacency matrices that have the same reachability matrix. However, in forming a digraph from a Reachability Matrix, a valuable digraph uniqueness can be achieved by applying the criterion that the digraph have the minimum possible number of edges that maintains reachability,represented by entries of 1 in the reachability matrix.