connected component

[water]

Could someone recommend a good module for enumerating all sets of connected components in an undirected graph? I could not determine which CPAN module would best serve. Thanks --

water

[spurperl]

The Graph:: family of classes on CPAN should be able to help you. Using Graph::Undirected you can use the connected_components() method.

[mrborisguy]

alright... i looked at Graph, which has a directed mode (i assume that's what you mean by uni-directed - i'm thinking uni is one, so one direction -, i could be wrong)
for an undirected graph, you could use $g->connected_components. i don't think it explicitly says how to get this for a directed graph. you'd have to roll your own... my idea is at least O(n^2) so there's probably a better way, but here ya go:

sub di_graph_connected {
    my $g = shift; # $g is of type 'Graph'
    my @verts = $g->vertices;
    my @pairs = ();
    foreach my $front ( @verts ) {
        foreach my $back ( @verts ) {
            push @pairs, [ $front, $back ] if $g->has_edge( $front, $b
+ack );
        }
    }

    return @pairs;
}

(code untested)
hope this helps!

[water]

Some time later, my own home-rolled hack, using a breadth first search:

package Algorithm::Graph;
use strict;
use Util qw(unique); # dedupes an array

sub connected_components {
    my ($g) = @_;
    die "g must be arrayref" unless ref $g eq 'ARRAY';
    die "empty graph?" unless @$g>0;
    my $adj;
    foreach my $pair (@$g) {
        die "g must be arrayref of arrayrefs" unless ref $pair eq 'ARR
+AY';
        die "g must be arrayref of 2-elem arrayrefs" unless @$pair == 
+2;
        my ( $x, $y ) = @$pair;
        $adj->{$x}{$y} = 1;
        $adj->{$y}{$x} = 1;
    }
    my %comp;
    for my $node ( keys %$adj ) {
        next if $comp{$node};
        $comp{$node} = $node;
        my @neighbors = keys %{ $adj->{$node} };
        while ( my $n = pop@ neighbors ) {
            die "set diff?" if $comp{$n} && $comp{$n} ne $node;
            $comp{$n} = $node;
            push( @neighbors, grep {! exists($comp{$_})} keys %{ $adj-
+>{$n} } );
        }
    }
    return [
        map {
            my $c = $_;
             [ sort grep { $comp{$_} eq $c } keys %comp ];
            } (sort (unique(values %comp)))
    ];
}

1;

And the tests

use strict;
use warnings FATAL => 'all';
use Test::Exception;
use Test::More tests => 12;

use_ok('Algorithm::Graph');

my %graphs = (
    '1,2' => [ [ 1, 2 ] ],
    'a|b|c|d' => [ [qw(a a)], [qw(b b)], [qw(c c)], [qw(d d)] ],
    '1,2,3,4,99|a,b,c,d,e,f,g,z' => [
        [qw(a b)], [qw(b c)], [qw(d c)], [qw(d e)], [qw(d f)], [qw(g d
+)],
        [qw(z g)], [ 1, 2 ], [ 3, 2 ], [ 4, 3 ], [ 99, 1 ]
    ],
    '1,2,3,4,99|apple,kiwi,pear|a,b,c,d,e,f,g,z' => [
        [qw(a b)], [qw(b c)],
        [qw(d c)], [qw(d e)],
        [qw(d f)], [qw(g d)],
        [qw(z g)], [ 1, 2 ],
        [ 3,  2 ], [ 4,       3 ],
        [ 99, 1 ], [ 'apple', 'pear' ],
        [ 'apple', 'kiwi' ]
    ],
);

foreach my $result ( keys %graphs ) {
    my $cc = Algorithm::Graph::connected_components( $graphs{$result} 
+);
    my $cc2 = join( "|", map { join( ",", @$_ ) } @$cc );
    is( $cc2, $result, $cc2 );
}

throws_ok { Algorithm::Graph::connected_components() } qr/arrayref/, '
+empty';
throws_ok { Algorithm::Graph::connected_components('fish') } qr/arrayr
+ef/,
  'fish';
throws_ok { Algorithm::Graph::connected_components( {} ) } qr/arrayref
+/, 'hash';
throws_ok { Algorithm::Graph::connected_components( [] ) } qr/empty/, 
+'[]';
throws_ok { Algorithm::Graph::connected_components( [ [] ] ) } qr/arra
+yref/,
  '[[]]';
throws_ok { Algorithm::Graph::connected_components( [ [ 1, 2, 3 ] ] ) 
+}
  qr/2-elem/, '[[1,2,3]]';
throws_ok { Algorithm::Graph::connected_components( [ [ 1, 2 ], [] ] )
+ }
  qr/2-elem/, '[[1,2],[]]';

Your mileage may vary.

water

[tlm]

Representing graphs as edge sets is not sufficiently general, because edge sets alone cannot represent graphs that have isolated nodes. That's why the standard mathematical definition of a graph consists of both a set of nodes and a set of edges formed from nodes in the set of nodes.

[water]

an inelegant cheesy solution, but I had this case covered by bogus self <-> self links, as shown by the test on 4 iso nodes, which return as 4 iso components.

# resulting components <--- graph
'a|b|c|d' => [ [qw(a a)], [qw(b b)], [qw(c c)], [qw(d d)] ],

again, a cheesy handrolled quick hack for what I needed, is all.

[tlm]

Last time I needed to do this, which was a few years ago, I ended up rolling my own, because anything I could find in CPAN was too slow. This may have changed since then, but an algorithm for this is not difficult; see the attached code.

Read more... (2 kB)