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package Graph::Maker::SmallWorldHK;
use strict;
use warnings;
use Carp qw/croak/;
use base qw/Graph::Maker/;
use Graph;
use Graph::Maker::Cycle;
use Math::Random::Free qw/random_uniform random_uniform_integer/;
our $VERSION = '0.01';
sub init
{
my ($self, %params) = @_;
my $n = delete($params{N}) || 0;
my $m = delete($params{M}) || 1;
my $m_0 = delete($params{M_0}) || $m;
my $p = delete($params{PR}) || 0;
my $callback = delete($params{callback}) || sub {};
my $gm = delete($params{graph_maker});
croak "graph_maker must be a reference to a function that creates a Graph.\n" if $gm && ref($gm) ne 'CODE';
$gm ||= sub { new Graph(@_); };
$m = $n if $m > $n;
my $g = $gm->(%params);
my @v = (1..$n);
my %deg;
$deg{$_} = 0 foreach (1..$n);
# MUST start with the $m_0 nodes connected to guarentee connectivity
for my $i(1..$m_0)
{
my $j = $i == $m_0 ? 1 : $i+1;
$g->add_edge($i, $j);
$g->add_edge($j, $i) unless $g->is_undirected();
$deg{$i}++;
$deg{$j}++;
}
# Preferential Attachment (PA) Growth
my $num_steps = $n - $m_0;
foreach my $t(1..$num_steps)
{
my $new_node = $m_0 + $t;
my $sel_node;
foreach my $j(1..$m)
{
# Triad Formation
if($sel_node && random_uniform() < $p)
{
my @succs = grep {$_ != $new_node} $g->successors($sel_node);
my $tri_node = $succs[random_uniform_integer(1, 0, @succs ? @succs-1 : 0)];
if($tri_node && !$g->has_edge($new_node, $tri_node))
{
$g->add_edge($new_node, $tri_node);
$g->add_edge($tri_node, $new_node) unless $g->is_undirected();
$deg{$new_node}++;
$deg{$tri_node}++;
next;
}
}
# Preferential Attachment
do
{
my $R = 0;
$R += $deg{$_} for (1..$t);
$R *= random_uniform();
my $i = 1;
my $cs = 0;
while($cs < $R)
{
$cs += $deg{$i};
$i++;
}
$sel_node = $i > 1 ? $i-1 : random_uniform_integer(1, 1, $m_0);
} until($new_node != $sel_node);
unless($g->has_edge($new_node, $sel_node))
{
$g->add_edge($new_node, $sel_node);
$g->add_edge($sel_node, $new_node) unless $g->is_undirected();
$deg{$new_node}++;
$deg{$sel_node}++;
}
}
$callback->($g, $new_node);
}
return $g;
}
Graph::Maker->add_factory_type( 'small_world_hk' => __PACKAGE__ );
1;
__DATA__
=head1 NAME
Graph::Maker::SmallWorldHK - Creates a small world graph according to Holmea, Beom & Kim
=head1 VERSION
Version 0.01
=cut
=head1 SYNOPSIS
Creates a small world graph according to Holmea, Beom & Kim's model.
A small world graph has an approximate power law degree distribution and a high clustering coefficient.
Holmea, Beom & Kim's can be seen as a super-set of th BA model as it also allows a "triangle formation"
phase to increase the clustering coefficient.
If the graph is directed then edges are added in both directions to create an undirected graph.
use strict;
use warnings;
use Graph;
use Graph::Maker;
use Graph::Maker::SmallWorldHK;
my $g = new Graph::Maker('small_world_hk', N => 10, M => 2, M_0 => 1, PR => 0, undirected => 1); # BA's model
my $g2 = new Graph::Maker('small_world_hk', N => 10, M => 2, M_0 => 1, PR => 0.25, undirected => 1);
# work with the graph
=head1 FUNCTIONS
=head2 new %params
Creates a small world graph with N nodes, initially starting with M_0 nodes and adding M (the minimum number of edges
per node) on each step probalistically doing a triangle formation with probability PR according to the Holmes, Beom & Kim model.
The recognized parameters are N, M, M_0, PR, graph_maker, and callback
any others are passed onto L<Graph>'s constructor.
If N is not given it defaults to 0.
If M is not given it defaults to 1.
If M_0 is not given it defaults to M.
If PR is not given it defaults to 0.
callback allows one to simulate the growth of a preferential attachment network, callback will be called each time
a node is added.
If graph_maker is specified it will be called to create the Graph class as desired (for example if you have a
subclass of Graph), this defaults to create a Graph with the parameters specified.
=cut
=head1 AUTHOR
Matt Spear, C<< <batman900+cpan at gmail.com> >>
=head1 BUGS
Please report any bugs or feature requests to
C<bug-graph-maker-smallworldhk at rt.cpan.org>, or through the web interface at
L<http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Graph-Maker>.
I will be notified, and then you'll automatically be notified of progress on
your bug as I make changes.
=head1 COPYRIGHT & LICENSE
Copyright 2008 Matt Spear, all rights reserved.
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
=cut
|
