Reachability Matrix: Difference between revisions
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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 | 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. | ||
Revision as of 12:54, 9 January 2022
In graph theory, reachability refers to the ability to get from one 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.
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.