202 lines
6.9 KiB
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202 lines
6.9 KiB
HTML
<HTML>
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<!--
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Copyright (c) Jeremy Siek 2000
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Strongly Connected Components</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1>
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<A NAME="sec:connected-components"></A><A NAME="sec:strongly-connected-components"></A>
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<img src="figs/python.gif" alt="(Python)"/>
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<TT>strong_components</TT>
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</H1>
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<PRE>
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<i>// named parameter version</i>
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template <class Graph, class ComponentMap, class P, class T, class R>
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typename property_traits<ComponentMap>::value_type
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strong_components(Graph& g, ComponentMap comp,
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const bgl_named_params<P, T, R>& params = <i>all defaults</i>)
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<i>// there is not a non-named parameter version of this function</i>
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</PRE>
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<P>
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The <TT>strong_components()</TT> functions compute the strongly
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connected components of a directed graph using Tarjan's algorithm
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based on DFS [<A
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HREF="bibliography.html#tarjan72:dfs_and_linear_algo">41</A>].
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</p>
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<P>
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The output of the algorithm is recorded in the component property
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map <TT>comp</TT>, which will contain numbers giving the component ID
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assigned to each vertex. The number of components is the return value
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of the function.
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</p>
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/strong_components.hpp"><TT>boost/graph/strong_components.hpp</TT></a>
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<P>
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<H3>Definitions</H3>
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<P>
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A <a name="def:strongly-connected-component"><b><I>strongly connected
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component</I></b></a> of a directed graph <i>G=(V,E)</i> is a maximal
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set of vertices <i>U</i> which is in <i>V</i> such that for every pair
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of vertices <i>u</i> and <i>v</i> in <i>U</i>, we have both a path
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from <i>u</i> to <i>v</i> and path from <i>v</i> to <i>u</i>. That is
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to say that <i>u</i> and <i>v</i> are reachable from each other.
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<P>
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<h3>Parameters</h3>
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IN: <tt>const Graph& g</tt>
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<blockquote>
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A directed graph. The graph type must be a model of <a
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href="VertexListGraph.html">Vertex List Graph</a> and <a
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href="IncidenceGraph.html">Incidence Graph</a>.<br>
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<b>Python</b>: The parameter is named <tt>graph</tt>.
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</blockquote>
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OUT: <tt>ComponentMap c</tt>
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<blockquote>
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The algorithm computes how many connected components are in the graph,
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and assigning each component an integer label. The algorithm then
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records which component each vertex in the graph belongs to by
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recording the component number in the component property map. The
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<tt>ComponentMap</tt> type must be a model of <a
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href="../../property_map/doc/WritablePropertyMap.html">Writable Property
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Map</a>. The value type should be an integer type, preferably the same
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as the <tt>vertices_size_type</tt> of the graph. The key type must be
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the graph's vertex descriptor type.<br>
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<b>Python</b>: Must be an <tt>vertex_int_map</tt> for the graph.<br>
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<b>Python default</b>: <tt>graph.get_vertex_int_map("component")</tt>
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</blockquote>
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<h3>Named Parameters</h3>
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UTIL: <tt>root_map(RootMap r_map)</tt>
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<blockquote>
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This is used by the algorithm to record the candidate root vertex for
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each vertex. By the end of the algorithm, there is a single root vertex
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for each component and <tt>get(r_map, v)</tt> returns the root
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vertex for whichever component vertex <tt>v</tt> is a member.
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The <TT>RootMap</TT> must be a <a
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href="../../property_map/doc/ReadWritePropertyMap.html">
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Read/Write Property Map</a>, where the key type and the value type are
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the vertex descriptor type of the graph.<br>
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<b>Default:</b> an <a
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href="../../property_map/doc/iterator_property_map.html">
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<tt>iterator_property_map</tt></a> created from a
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<tt>std::vector</tt> of vertex descriptors of size
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<tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
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map.<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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UTIL: <tt>discover_time_map(TimeMap t_map)</tt>
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<blockquote>
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This is used by the algorithm to keep track of the DFS ordering
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of the vertices. The <TT>TimeMap</TT> must be a model
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of <a href="../../property_map/doc/ReadWritePropertyMap.html"> Read/Write
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Property Map</a> and its value type must be an integer type. The key
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type must be the vertex descriptor type of the graph.<br>
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<b>Default:</b>an <a
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href="../../property_map/doc/iterator_property_map.html">
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<tt>iterator_property_map</tt></a> created from a
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<tt>std::vector</tt> of integers with size
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<tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
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map.<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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UTIL: <tt>color_map(ColorMap c_map)</tt>
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<blockquote>
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This is used by the algorithm to keep track of its progress through
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the graph. The type <tt>ColorMap</tt> must be a model of <a
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href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
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Property Map</a> and its key type must be the graph's vertex
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descriptor type and the value type of the color map must model
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<a href="./ColorValue.html">ColorValue</a>.<br>
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<b>Default:</b> an <a
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href="../../property_map/doc/iterator_property_map.html">
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<tt>iterator_property_map</tt></a> created from a
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<tt>std::vector</tt> of <tt>default_color_type</tt> of size
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<tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
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map.<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
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<blockquote>
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This maps each vertex to an integer in the range <tt>[0,
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num_vertices(g))</tt>. This parameter is only necessary when a
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default is used for one of the other named parameters. The type
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<tt>VertexIndexMap</tt> must be a model of <a
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href="../../property_map/doc/ReadablePropertyMap.html">Readable Property
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Map</a>. The value type of the map must be an integer type. The
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vertex descriptor type of the graph needs to be usable as the key
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type of the map.<br>
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<b>Default:</b> <tt>get(vertex_index, g)</tt>
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Note: if you use this default, make sure your graph has
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an internal <tt>vertex_index</tt> property. For example,
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<tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
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not have an internal <tt>vertex_index</tt> property.
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<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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<H3>Complexity</H3>
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<P>
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The time complexity for the strongly connected components algorithm is
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<i>O(V + E)</i>.
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<P>
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<h3>See Also</h3>
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<a href="./connected_components.html"><tt>connected_components()</tt></a>
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and <a href="./incremental_components.html"><tt>incremental_components()</tt></a>
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<H3>Example</H3>
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<P>
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See <a
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href="../example/strong_components.cpp"><tt>examples/strong_components.cpp</tt></a>.
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<br>
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<HR>
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<TABLE>
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<TR valign=top>
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<TD nowrap>Copyright © 2000-2001</TD><TD>
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<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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