sub graph_from_degree_sequence {
  # create edge hash and empty graph
  my $v = 'a';
  my %e = map +($v++ => $_), @_;
  my %g;

  # algorithm is as follows:

  while (1) {
    # sort the vertices of the graph by degree (high to low)
    my @order = sort { $e{$b} <=> $e{$a} } keys %e;

    # if the degree of the vertex with the highest
    # degree is zero, then we're done
    last if $e{$order[0]} == 0;

    # otherwise, connect this vertex to the next N
    # vertices (in order of their degrees), where N is
    # the degree of the vertex with the highest degree
    for (1 .. $e{$order[0]}) {
      # decrement the connected vertex's degree, and
      # check to see if it's less than zero -- if it
      # is, this degree sequence cannot produce a graph
      --$e{$order[$_]} < 0 and return;

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

    # set the degree of this vertex to zero, which
    # means it is not to be connected to anymore
    $e{$order[0]} = 0;
  }

  return \%g;
}
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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;
}
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