Fletch is correct; by your own description, the only code that you posted is not the even the code that produces the warning. Please post more details. Often, when reducing large code to a concise example of a problem, you will find the solution yourself.

That said, I can see a few possible problems.

1. You mention Graph::Undirected, which implies that your graphs should be undirected, but your example code uses Graph->new(), which creates *directed* graphs.
2. Graph::Writer::Dot does not correctly handle undirected graphs; it treats them as if they were directed. This will not produce any warning; it will just cause GraphViz to render the graph's edges with arrows. My casual testing indicates that this simple patch will correct the problem:

   --- Graph/Writer/Dot.pm_original    Fri Jun 14 01:54:05 2002
   +++ Graph/Writer/Dot.pm    Mon Nov 15 10:31:35 2004
   @@ -68,13 +68,15 @@
        my %attributes;
        my @keys;
    
   +    my $arrow = ($graph->directed) ? '->' : '--';
   +    my $gname = ($graph->directed) ? 'digraph' : 'graph';
    
        #----------------------------------------------------------------
   +---
        # If the graph has a 'name' attribute, then we use that for the
        # name of the digraph instance. Else it's just 'g'.
        #----------------------------------------------------------------
   +---
        $gn = $graph->has_attribute('name') ? $graph->get_attribute('name
   +') : 'g';
   -    print $FILE "digraph $gn\n{\n";
   +    print $FILE "$gname $gn\n{\n";
    
        #----------------------------------------------------------------
   +---
        # Dump out any overall attributes of the graph
   @@ -114,7 +116,7 @@
        while (@edges > 0)
        {
        ($from, $to) = splice(@edges, 0, 2);
   -    print $FILE "  $from -> $to";
   +    print $FILE "  $from $arrow $to";
        %attributes = $graph->get_attributes($from, $to);
        @keys = grep(exists $attributes{$_}, @{$valid_attributes{'edge'}}
   +);
        if (@keys > 0)
   [download]

3. You may be using the wrong syntax to invoke methods on the objects stored in the %graph hash. Here is a working example program, to demonstrate the syntax:

   #!/usr/bin/perl
   use warnings 'all';
   use strict;
   use Graph::Undirected;
   use Graph::Writer::Dot;
   
   my @areas = qw(
     America
     Britain
     Chile
   );
   my @verts = qw(
     Phone_Company
     Cellular_Networks
     Government
     Internet
     Rural_Users
   );
   
   my %graph; # Hash of Graph::Undirected objects.
   foreach my $area (@areas) {
     $graph{$area} = Graph::Undirected->new();
     $graph{$area}->add_vertex($_) foreach @verts;
   }
   
   $graph{America}->add_edge(@verts[0,1]);
   $graph{America}->add_edge(@verts[1,2]);
   $graph{America}->add_edge(@verts[3,0]);
   $graph{America}->add_edge('Government', 'Internet');
   
   $graph{Britain}->add_edge(@verts[0,2]);
   $graph{Britain}->add_edge(@verts[1,2]);
   $graph{Britain}->add_edge(@verts[3,2]);
   
   for ($graph{Chile}) {
     $_->add_edge(@verts[0,1]);
     $_->add_edge(@verts[0,2]);
     $_->add_edge(@verts[0,3]);
     $_->add_edge(@verts[1,2]);
     $_->add_edge(@verts[1,3]);
     $_->add_edge(@verts[2,3]);
   }
   
   my $writer = Graph::Writer::Dot->new();
   foreach my $area (@areas) {
     $writer->write_graph($graph{$area}, "$area.dot");
   }
   [download]

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