sub graph_from_degree_sequence {
  my $v = 'a';
  my %e = map +($v++ => $_), @_;
  my %g;

  while (1) {
    # this will only have non-zero-degree vertices
    my @order = sort { $e{$b} <=> $e{$a} } keys %e

      # if there aren't any, we're done
      or last;

    # if there aren't enough available vertices to
    # connect to, this degree sequence is no good
    return if @order < $e{$order[0]};

    for (1 .. $e{$order[0]}) {
      # each vertex's degree is guaranteed to be at
      # least 1, so if it becomes 0, make it ineligible
      --$e{$order[$_]} or delete $e{$order[$_]};

      # create the edges between the two
      push @{ $g{$order[0]} }, $order[$_];
      push @{ $g{$order[$_]} }, $order[0];
    }

    delete $e{$order[0]};
  }

  return \%g;
}