True. The problem is SPT_Dijkstra in Graph is sometimes wrong.

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };
use Syntax::Construct qw{ // };

use Graph;

my %graph;
my $first;

# Handle the sample data where there are sometimes less than 4 neighbo
+urs.
while (<DATA>) {
    my ($node, @neighbours) = split;
    $first //= $node;
    my $distance = 1;
    for my $neighbour (@neighbours) {
        if (not exists $graph{$node}{$neighbour}
            or $graph{$node}{$neighbour} < $distance) {
            $_ = $distance for $graph{$node}{$neighbour},
                               $graph{$neighbour}{$node};
        }
        $distance++;
    }
}


my $g = 'Graph::Undirected'->new;
for my $u (keys %graph) {
    for my $v (keys %{ $graph{$u} }) {
        $g->add_weighted_edge($u, $v, $graph{$u}{$v});
    }
}

my $dij = $g->SPT_Dijkstra($first);
my %weights = ($first => 0);
$weights{$_} //= $dij->get_vertex_attribute($_, 'weight') for keys %gr
+aph;
say join ' ', sort { $weights{$a} <=> $weights{$b} }
              keys %weights;

__DATA__
O1 O3 O5 O11 O73
O2 O72 O54 O12 O7
O3 O1 O6 O5 O12
O5 O1 O3
O6 O3
O7 O2
O11 O1
O12 O2 O3
O54 O2
O72 O2
O73 O1
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