Monks,

I have written the following code that creates a graph using the Graph::Directed package and generates a distance matrix accordingly:

use Graph::Directed;
use warnings;
use strict;

# Instantiate
my $G = new Graph::Directed;

# Metabolite Create graph
$G = $G->add_edge("E1", "E2");
$G = $G->add_edge("E2", "E3");
$G = $G->add_edge("E3", "E1");
$G = $G->add_edge("E3", "E2");
$G = $G->add_edge("E2", "E2");
$G = $G->add_edge("E3", "E3");

# Weight edges (constant)
$G->set_attribute("weight", "E1", "E2", 1);
$G->set_attribute("weight", "E2", "E3", 1);
$G->set_attribute("weight", "E3", "E1", 1);
$G->set_attribute("weight", "E3", "E2", 1);
$G->set_attribute("weight", "E2", "E2", 1);
$G->set_attribute("weight", "E3", "E3", 1);

# Give meaningful names to edges
$G->set_attribute("name", "E1", "E2", "C");
$G->set_attribute("name", "E2", "E3", "F");
$G->set_attribute("name", "E3", "E1", "A");
$G->set_attribute("name", "E3", "E2", "F");
$G->set_attribute("name", "E2", "E2", "C,E,F");
$G->set_attribute("name", "E3", "E3", "A,F");

# Print some info about graph
print "GRAPH (", scalar $G->vertices, " vertices):\n", $G, "\n\n";

# All Pairs Shortest Path
my $APSP = $G->APSP_Floyd_Warshall;
print "ALL AVAILABLE PAIRS:\n", $APSP, "\n\n";

print "DISTANCE MATRIX:\n";
print "\t", join ("\t", $G->vertices), "\n";
foreach my $rowVtx ($G->vertices) {
    print "$rowVtx\t";
    foreach my $colVtx ($G->vertices) {
    $APSP->get_attribute("weight", $rowVtx, $colVtx);
    print $APSP->get_attribute("weight", $rowVtx, $colVtx), "\t";
    }
    print "\n";
}
[download]

The following output is produced:

GRAPH (3 vertices):
E1-E2,E2-E2,E2-E3,E3-E1,E3-E2,E3-E3

ALL AVAILABLE PAIRS:
E1-E1,E1-E2,E1-E3,E2-E1,E2-E2,E2-E3,E3-E1,E3-E2,E3-E3

DISTANCE MATRIX:
        E1      E2      E3
E1      0       1       2
E2      2       0       1
E3      1       1       0
[download]

The distance matrix is exactly correct apart from the diagonal (E1-E1, E2-E2, E3-E3). By correct I mean it isn't the result I want as it is correct in terms of graph theory. What I want is for the cell E1,E1 = 3, the cell E2,E2 = 1 and E3,E3 = 1. Obviously the distance from E1->E1 is zero as the start nodes and end nodes are equal - however, I wish to intorduce the constraint that the search must leave the start node before returning (a domain specific feature of the problem). The required matrix therfore is below:

DISTANCE MATRIX:
        E1      E2      E3
E1      3       1       2
E2      2       1       1
E3      1       1       1
[download]

Thus to get from E1->E1 in the above graph you must go E1->E2->E3->E1, the distance of which equals 3 (all arcs have a weight/cost of 1) as required. The corresponding paths for E2 and E3 have a distance of just 1 because they have self referencing arcs.

The question: can anyone think of a way of obtaining the required result (and thus placing the constraint on the algorithm) with the minimum effort - preferably whilst staying within the bounds of Graph::Directed.

Best wishes,