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