Description:  Conjuring on an adjacency matrix (thanks to Math::MatrixReal), this snippet finds every couple of nodes (i, j) such that there's a path from i to j. The matrix $sum is called transitive closure of the graph $graph. 
#!/usr/bin/perl
# Transitive closure of a directed graph
use strict;
use Math::MatrixReal;
my $n = 4; # Matrix' size
my $graph = Math::MatrixReal>new_from_string( <<'MATRIX' );
[ 0 1 0 1 ]
[ 0 0 1 0 ]
[ 0 0 0 0 ]
[ 1 1 0 0 ]
MATRIX
my $sum = $graph>shadow();
my $p = $graph>shadow();
$p>one();
# "One Ring to rule them all, One Ring to find them..."
# Sum of A^i, for i = 0..n1 (A is the adjacency matrix of our graph)
foreach (0 .. ($n  1)) {
$p = $p * $graph;
$sum = $sum + $p;
}
# Finished.
# Now we print every couple (i, j) such that
# there's a path from i to j.
foreach my $i (1..$n) {
foreach my $j (1..$n) {
print "There's a path from $i to $j.\n" if $sum>element( $i,
+$j );
}
}


Replies are listed 'Best First'.  

Re: Transitive closure
by Zaxo (Archbishop) on Sep 10, 2001 at 17:15 UTC  
by larsen (Parson) on Sep 11, 2001 at 11:19 UTC 