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<Title>Boost Graph Library: make_connected</Title>
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<H1><tt>make_connected</tt></H1>

<p>

<pre>
template &lt;typename Graph, typename VertexIndexMap, typename AddEdgeVisitor&gt;
make_connected(Graph& g, VertexIndexMap vm, AddEdgeVisitor& vis);
</pre>

<p>

A undirected graph <i>G</i> is connected if, for every pair of vertices 
<i>u,v</i> in <i>G</i>, there is a path from <i>u</i> to <i>v</i>. 
<tt>make_connected</tt> adds the minimum number of edges needed to make the 
input graph connected. The algorithm first identifies all of the 
<a href="./connected_components.html">connected components</a> in the graph,
then adds edges to connect those components together in a path. For example, if
a graph contains three connected components <i>A</i>, <i>B</i>, and <i>C</i>, 
<tt>make_connected</tt> will add two edges. The two edges added might consist 
of one connecting a vertex in <i>A</i> with a vertex in <i>B</i> and one 
connecting a vertex in <i>B</i> with a vertex in <i>C</i>.
<p>
The default behavior of <tt>make_connected</tt> is to modify the graph 
<tt>g</tt> by calling <tt>add_edge(u,v,g)</tt> for every pair of vertices 
<i>(u,v)</i> where an edge needs to be added to connect <tt>g</tt>. This 
behavior can be overriden by providing a vistor as the <tt>AddEdgeVisitor</tt> 
parameter. The only requirement for an <tt>AddEdgeVisitor</tt> is that it 
define a member function with the following signature:
<pre>
template &lt;typename Graph, typename Vertex&gt;
void visit_vertex_pair(Vertex u, Vertex v, Graph& g);
</pre>
This event point can also be used as a hook to update the underlying edge
index map automatically as edges are added. See the 
documentation for the <a href="./AddEdgeVisitor.html">AddEdgeVisitor</a> 
concept for more information.


<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/make_connected.hpp">
<TT>boost/graph/make_connected.hpp</TT>
</a>

<h3>Parameters</h3>

IN/OUT: <tt>Graph&amp; g</tt>

<blockquote>
An undirected graph. The graph type must be a model of <a
href="VertexListGraph.html">Vertex List Graph</a>, <a
href="IncidenceGraph.html">Incidence Graph</a>, and
a <a href="MutableGraph.html">Mutable Graph</a><br>
</blockquote>

IN: <tt>VertexIndexMap vm</tt>

<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps vertices from <tt>g</tt> to distinct integers in the range 
<tt>[0, num_vertices(g) )</tt><br>
<b>Default</b>: <tt>get(vertex_index,g)</tt><br>
</blockquote>

IN: <tt>AddEdgeVisitor</tt>

<blockquote>
A model of <a href="AddEdgeVisitor.html">AddEdgeVisitor
</a>.<br>
<b>Default</b>: <tt>default_add_edge_visitor</tt>, a class defines 
<tt>visit_vertex_pair</tt> to dispatch
its calls to <tt>add_edge</tt>.
</blockquote>


<h3>Complexity</h3>

On a graph with <i>n</i> vertices and <i>m</i> edges, <tt>make_connected</tt> 
runs in time <i>O(n + m)</i>

<H3>Example</H3>

<P>
<a href="../example/make_connected.cpp">
<TT>../example/make_connected.cpp</TT>
</a>

<h3>See Also</h3>

<a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a>

<br>
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Copyright &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
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