NAME

       Graph::Maker::SmallWorldK - Creates a small world graph using Kleinberg's model in
       2-dimensions

VERSION

       Version 0.01

SYNOPSIS

       Creates a small world graph according to Kleinberg's long-range connection model.  In
       Kleinberg's model a small world graph is connected to nodes within manhattan (L1) distance
       P and has Q long range contacts referred to as K(N, P, Q, alpha) or K*(N, P, Q, alpha) (if
       it wraps-around).  In addition Kleinberg's model gives all nodes a position so that
       routing can be done efficiently using a greedy algorithm, these positions are set in the
       'pos' attribute for the vertices.  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::SmallWorldK;

               my $g = new Graph::Maker('small_world_k', N => 10, P => 2, undirected => 1);
               my $g2 = new Graph::Maker('small_world_k', N => 10, P => 2, Q => 1, alpha => 2.1, undirected => 1);
               # work with the graph

FUNCTIONS

   new %params
       Creates a small world graph with N^2 nodes in a 2-d grid, with connections to nodes within
       P manhattan units of distance, and Q random long-range connections to nodes determined by
       d(u, v) ** -alpha (where d is the manhattan distance) according to Kleinberg's model (the
       grid wraps-around if cyclic is specified).  The recognized parameters are N, P, Q, cyclic,
       graph_maker,  and alpha any others are passed onto Graph's constructor.  If N is not given
       it defaults to 0.  If P is not given it defaults to 1.  If Q is not given it defaults to
       0.  If alpha is not given it defaults to 2 (2 <= alpha <= 3 allows poly-logarithmic
       routing using a local greedy algorithm).  If cyclic is set then the "edges" of the grid
       are connected.  The vertex attribute pos will be set to an array reference of the nodes
       d-dimensional position.  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.

AUTHOR

       Matt Spear, "<batman900+cpan at gmail.com>"

BUGS

       Please report any bugs or feature requests to "bug-graph-maker-SmallWorldK at
       rt.cpan.org", or through the web interface at
       <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.

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.