I'm not seeing the logic behind that output datastructure.

Some questions:

• Why is the cluster ID in a hash, when it is a simple integer count? An array would make sense to me.
• Why is the element before the cluster? Not all clusters will have the same number of elements, and as is, you can't separate one cluster from the rest and pass it to a sub.
• Are there any advantages to the current order that I do not see? You can get a hash of clusters that have an Nth element, but Nth elements don't mean much since the order of elements in a cluster is arbitrary.

The way I would do this is an AoA structure, with the indexes reversed:

my $data = shift;
my @clusters;
my $elementsAlreadyUsed = [];
while (my $nextCluster = findNextCluster($data, $elementsAlreadyUsed))
{
  push @clusters, nextCluster;
}

# Loop over each cluster
for my $clusterID (0.. $#clusters)
{
  print "Cluster $clusterID (#". ($clusterID +1) . ")\n";  

  # Print the elements contained in the cluster
  print "\tContains element(s): ". (join ', ', @{$clusters[$clusterID]
+}) . "\n";
}

sub findNextCluster
{
  my $data = shift;
  my $elementsUsed = shift;

  # Pick first unused element to start from.
    # Return undef if all elements are used.
  # DFS or BFS over data connected to the start element;

  return BFSResultArrayRef($data, $startElement);
}
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Thusly, $someElement = $clusters[$clusterIndex][$elementIndex];
and $arrayRefOfAllElementsInCluster = $clusters[$clusterIndex];
and $numElementsInCluster = scalar @{$clusters[$clusterIndex]};