template<typename RandomGenerator, typename Graph>
class plod_iterator
{
public:
  typedef std::input_iterator_tag iterator_category;
  typedef std::pair<vertices_size_type, vertices_size_type> value_type;
  typedef const value_type& reference;
  typedef const value_type* pointer;
  typedef void difference_type;

  plod_iterator();
  plod_iterator(RandomGenerator& gen, vertices_size_type n,
                double alpha, double beta, bool allow_self_loops = false);
  // Iterator operations
  reference operator*() const;
  pointer operator->() const;
  plod_iterator& operator++();
  plod_iterator operator++(int);
  bool operator==(const plod_iterator& other) const;
  bool operator!=(const plod_iterator& other) const;
}; 

This class template implements a generator for scale-free graphs using the Power Law Out Degree (PLOD) algorithm [63], suitable for initializing an adjacency_list or other graph structure with iterator-based initialization. A scale-free graph typically has a very skewed degree distribution, where few vertices have a very high degree and a large number of vertices have a very small degree. Many naturally evolving networks, such as the World Wide Web, are scale-free graphs, making these graphs a good model for certain networking problems.

The Power Law Out Degree (PLOD) algorithm generates a scale-free graph from three parameters, n, alpha, and beta, by allocating a certain number of degree "credits" to each vertex, drawn from a power-law distribution. It then creates edges between vertices, deducting a credit from each involved vertex (in the undirected case) or the source vertex (in the directed case). The number of credits assigned to a vertex is: beta*x^-alpha, where x is a random value between 0 and n-1. The value of beta controls the y-intercept of the curve, so that increasing beta increases the average degree of vertices. The value of alpha controls how steeply the curve drops off, with larger values indicating a steeper curve. The web graph, for instance, has alpha ~ 2.72.

Where Defined

Constructors

plod_iterator();

plod_iterator(RandomGenerator& gen, vertices_size_type n,
              double alpha, double beta, bool allow_self_loops = false);

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/plod_generator.hpp>
#include <boost/random/linear_congruential.hpp>

typedef boost::adjacency_list<> Graph;
typedef boost::plod_iterator<boost::minstd_rand, Graph> SFGen;

int main()
{
  boost::minstd_rand gen;
  // Create graph with 100 nodes 
  Graph g(SFGen(gen, 100, 2.5, 1000), SFGen(), 100);
  return 0;
}