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Reachability Matrix: Difference between revisions
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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 | 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 | 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. | ||