package SNA::Network::Algorithm::PageRank;
use strict;
use warnings;
require Exporter;
use base qw(Exporter);
our @EXPORT = qw(calculate_pageranks calculate_weighted_pageranks);
use List::Util qw(sum);
=head1 NAME
SNA::Network::Algorithm::PageRank - implementation of the PageRank algorithm
=head1 SYNOPSIS
use SNA::Network;
my $net = SNA::Network->new();
$net->load_from_pajek_net($filename);
...
$net->calculate_pageranks();
=head1 METHODS
The following methods are added to L<SNA::Network>.
=head2 calculate_pageranks
Calculates PageRank values for all nodes.
Stores the values under the hash entry B<pagerank> for each node object.
You can pass named parameters to control the algorithm:
B<iterations> specifies the number of iterations to use, and defaults to 20.
B<damping> specifies the damping factor of PageRank and defaults to 0.15.
=cut
sub calculate_pageranks {
my ($self, %params) = @_;
my $iterations = $params{iterations} || 20;
my $damping = $params{damping};
$damping = 0.15 unless defined $damping;
my $num_nodes = int $self->nodes;
# sink nodes (nodes without successors) result into a random jumo
my @sink_nodes = grep { $_->out_degree == 0 } $self->nodes;
my @non_sinks = grep { $_->out_degree > 0 } $self->nodes;
# start with 1.0 for each node
foreach my $node ($self->nodes) {
$node->{pagerank} = 1.0; }
# iterative approximation
for (1 .. $iterations) {
my $sinks_pr = sum 0, map { $_->{pagerank} } @sink_nodes;
my $pr_from_sinks = $sinks_pr / $num_nodes;
my $flowing_pr = $num_nodes - $sinks_pr;
my $pr_from_jumps = $flowing_pr * $damping / $num_nodes;
foreach my $node ($self->nodes) {
$node->{new_pr} = $pr_from_jumps + $pr_from_sinks;
}
foreach my $node (@non_sinks) {
my $outgoing_pr = (1 - $damping) * $node->{pagerank} / $node->out_degree;
foreach my $successor ($node->outgoing_nodes) {
$successor->{new_pr} += $outgoing_pr;
}
}
# copy new values
foreach my $node ($self->nodes) {
$node->{pagerank} = $node->{new_pr};
}
}
}
=head2 calculate_weighted_pageranks
Intuitive extension of PageRank to weighted networks.
Same as above, but treating edge weights as relative probabilities
for the node transitions.
Stores the values under the hash entry B<pagerank> for each node object,
the same key as above!
You can pass the same parameters as above.
On a weighted network, you usually want this method's values'.
=cut
sub calculate_weighted_pageranks {
my ($self, %params) = @_;
my $iterations = $params{iterations} || 20;
my $damping = $params{damping};
$damping = 0.15 unless defined $damping;
my $num_nodes = int $self->nodes;
# sink nodes (nodes without successors) result into a random jumo
my @sink_nodes = grep { $_->out_degree == 0 } $self->nodes;
my @non_sinks = grep { $_->out_degree > 0 } $self->nodes;
# start with 1.0 for each node
foreach my $node ($self->nodes) {
$node->{pagerank} = 1.0;
}
# iterative approximation
for (1 .. $iterations) {
my $sinks_pr = sum 0, map { $_->{pagerank} } @sink_nodes;
my $pr_from_sinks = $sinks_pr / $num_nodes;
my $flowing_pr = $num_nodes - $sinks_pr;
my $pr_from_jumps = $flowing_pr * $damping / $num_nodes;
foreach my $node ($self->nodes) {
$node->{new_pr} = $pr_from_jumps + $pr_from_sinks;
}
foreach my $node (@non_sinks) {
my $outgoing_pr = (1 - $damping) * $node->{pagerank} / $node->weighted_out_degree;
foreach my $outgoing_link ($node->outgoing_edges) {
$outgoing_link->target->{new_pr} += $outgoing_pr * $outgoing_link->weight;
}
}
# copy new values
foreach my $node ($self->nodes) {
$node->{pagerank} = $node->{new_pr};
}
}
}
=head1 AUTHOR
Darko Obradovic, C<< <dobradovic at gmx.de> >>
=head1 BUGS
Please report any bugs or feature requests to C<bug-sna-network-node at rt.cpan.org>, or through
the web interface at L<http://rt.cpan.org/NoAuth/ReportBug.html?Queue=SNA-Network>. I will be notified, and then you'll
automatically be notified of progress on your bug as I make changes.
=head1 SUPPORT
You can find documentation for this module with the perldoc command.
perldoc SNA::Network
You can also look for information at:
=over 4
=item * RT: CPAN's request tracker
L<http://rt.cpan.org/NoAuth/Bugs.html?Dist=SNA-Network>
=item * AnnoCPAN: Annotated CPAN documentation
L<http://annocpan.org/dist/SNA-Network>
=item * CPAN Ratings
L<http://cpanratings.perl.org/d/SNA-Network>
=item * Search CPAN
L<http://search.cpan.org/dist/SNA-Network>
=back
=head1 ACKNOWLEDGEMENTS
=head1 COPYRIGHT & LICENSE
Copyright 2009 Darko Obradovic, all rights reserved.
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
=cut
1; # End of SNA::Network::Algorithm::PageRank