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      Authors: Douglas Gregor
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               Andrew Lumsdaine
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<Head>
  <Title>Boost Graph Library: Erd&ouml;s-Renyi Generator</Title>
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<tt>erdos_renyi_iterator</tt>

<br>

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

  erdos_renyi_iterator();
  erdos_renyi_iterator(RandomGenerator&amp; gen, vertices_size_type n,
                       double fraction = 0.0, bool allow_self_loops = false);
  erdos_renyi_iterator(RandomGenerator&amp; gen, vertices_size_type n,
                       edges_size_type m, bool allow_self_loops = false);

  // Iterator operations
  reference operator*() const;
  pointer operator-&gt;() const;
  erdos_renyi_iterator&amp; operator++();
  erdos_renyi_iterator operator++(int);
  bool operator==(const erdos_renyi_iterator&amp; other) const;
  bool operator!=(const erdos_renyi_iterator&amp; other) const;
}; 
</PRE>

<p> This class template implements a generator for Erd&ouml;s-Renyi
graphs, suitable for initializing an <a
href="adjacency_list.html"><tt>adjacency_list</tt></a> or other graph
structure with iterator-based initialization. An Erd&ouml;s-Renyi
graph <em>G = (n, p)</em> is a graph with <em>n</em> vertices
that. The probability of having an edge <em>(u, v)</em> in <em>G</em>
is <em>p</em> for any vertices <em>u</em> and <em>v</em>. Typically,
there are no self-loops, but the generator can optionally introduce
self-loops with probability <em>p</em>. This generator will not
produce any parallel edges and will produce edges in sorted order (as
required by, e.g., the <a
href="compressed_sparse_row.html"><tt>compressed_sparse_row_graph</tt></a>).</p>

<p>Erd&ouml;s-Renyi graphs typically exhibit very little
structure. For this reason, they are rarely useful in modeling
real-world problems. However, they are often used when determining
the theoretical complexity of complex graph algorithms.</p>

<p>If you want the possibility of generating parallel edges and don't
care about sorted order, use the <a
href="erdos_renyi_generator.html"><tt>erdos_renyi_iterator</tt></a>.</p>

<h3>Where Defined</h3>

<a href="../../../boost/graph/erdos_renyi_generator.hpp"><tt>boost/graph/erdos_renyi_generator.hpp</tt></a>

<h3>Constructors</h3>

<a name="default-constructor"/>
<pre>erdos_renyi_iterator();</pre>
<blockquote>
Constructs a past-the-end iterator.
</blockquote>

<pre>
erdos_renyi_iterator(RandomGenerator&amp; gen, vertices_size_type n,
                     double fraction = 0.0, bool allow_self_loops = false);
</pre>
<blockquote>
Constructs an Erd&ouml;s-Renyi generator iterator that creates a
graph with <tt>n</tt> vertices and a given <tt>fraction</tt> of the
total number of edges that a simple graph may have.
<tt>probability</tt>. Random vertices and edges are selected using the
random number generator <tt>gen</tt>. Self-loops are permitted only when
<tt>allow_self_loops</tt> is <tt>true</tt>.
</blockquote>

<pre>
erdos_renyi_iterator(RandomGenerator&amp; gen, vertices_size_type n,
                     edges_size_type m, bool allow_self_loops = false);
</pre>
<blockquote>
Constructs an Erd&ouml;s-Renyi generator iterator that creates a
graph with <tt>n</tt> vertices and <tt>m</tt> edges.
<tt>probability</tt>. Random vertices and edges are selected using the
random number generator <tt>gen</tt>. Self-loops are permitted only when
<tt>allow_self_loops</tt> is <tt>true</tt>.
</blockquote>

<H3>Example</H3>

<pre>
#include &lt;boost/graph/adjacency_list.hpp&gt;
#include &lt;boost/graph/erdos_renyi_generator.hpp&gt;
#include &lt;boost/random/linear_congruential.hpp&gt;

typedef boost::adjacency_list&lt;&gt; Graph;
typedef boost::erdos_renyi_iterator&lt;boost::minstd_rand, Graph&gt; ERGen;

int main()
{
  boost::minstd_rand gen;
  // Create graph with 100 nodes and edges with probability 0.05
  Graph g(ERGen(gen, 100, 0.05), ERGen(), 100);
  return 0;
}
</pre>

<br>
<HR>
<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 2005</TD><TD>
<A HREF="http://www.boost.org/people/doug_gregor.html">Doug Gregor</A>, Indiana University (<script language="Javascript">address("cs.indiana.edu", "dgregor")</script>)<br>
  <A HREF="https://homes.cs.washington.edu/~al75">Andrew Lumsdaine</A>,
Indiana University (<script language="Javascript">address("osl.iu.edu", "lums")</script>)
</TD></TR></TABLE>

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