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- <Head>
- <Title>Boost Graph Library: Fruchterman-Reingold Force-Directed Layout</Title>
- <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
- ALINK="#ff0000">
- <IMG SRC="../../../boost.png"
- ALT="C++ Boost" width="277" height="86">
- <BR Clear>
- <img src="figs/python.gif" alt="(Python)"/>
- <TT>fruchterman_reingold_force_directed_layout</TT>
- </H1>
- <P>
- <PRE>
- <i>// named parameter version</i>
- template<typename Graph, typename PositionMap, typename Topology, typename Param,
- typename Tag, typename Rest>
- void
- fruchterman_reingold_force_directed_layout
- (const Graph& g,
- PositionMap position,
- const Topology& space,
- const bgl_named_params<Param, Tag, Rest>& params);
- <i>// non-named parameter version</i>
- template<typename Graph, typename PositionMap, typename Topology,
- typename AttractiveForce, typename RepulsiveForce,
- typename ForcePairs, typename DisplacementMap, typename Cooling>
- void
- fruchterman_reingold_force_directed_layout
- (const Graph& g,
- PositionMap position,
- const Topology& space,
- AttractiveForce fa,
- RepulsiveForce fr,
- ForcePairs fp,
- Cooling cool,
- DisplacementMap displacement);
- template<typename Graph, typename PositionMap, typename Topology>
- void
- fruchterman_reingold_force_directed_layout(const Graph& g,
- PositionMap position,
- Topology& space,
- Dim width,
- Dim height);
- </PRE>
- <P> This algorithm [<A
- HREF="bibliography.html#fruchterman91">58</A>] performs layout of
- unweighted, undirected graphs. Unlike the <a
- href="kamada_kawai_spring_layout.html">Kamada-Kawai</a> layout
- algorithm, this algorithm directly supports the layout of disconnected
- graphs (but see the <tt>force_pairs</tt> named parameter). It is a
- <em>force-directed</em> algorithm, meaning that vertex layout is
- determined by the forces pulling vertices together and pushing them
- apart. Attractive forces occur between adjacent vertices only, whereas
- repulsive forces occur between every pair of vertices. Each iteration
- computes the sum of the forces on each vertex, then moves the vertices
- to their new positions. The movement of vertices is mitigated by the
- <i>temperature</i> of the system for that iteration: as the algorithm
- progresses through successive iterations, the temperature should
- decrease so that vertices settle in place. The cooling schedule,
- attractive forces, and repulsive forces can be provided by the user.
- <p> The vertices are often placed randomly prior to execution of this algorithm via <a href="random_layout.html"><tt>random_graph_layout</tt></a>.
- <h3>Where Defined</h3>
- <a href="../../../boost/graph/fruchterman_reingold.hpp"><tt>boost/graph/fruchterman_reingold.hpp</tt></a>
- <h3>Parameters</h3>
- IN: <tt>const Graph& g</tt>
- <blockquote>
- The graph object on which the algorithm will be applied.
- The type <tt>Graph</tt> must be a model of
- <a href="./VertexAndEdgeListGraph.html">Vertex And Edge List Graph</a>.<br>
- <b>Python</b>: This parameter is named <tt>graph</tt> in Python.
- </blockquote>
- IN/OUT: <tt>PositionMap position</tt>
- <blockquote>
- The property map that stores the position of each vertex. It should
- typically be initialized with the vertices at random locations (use
- <a href="random_layout.html"><tt>random_graph_layout</tt></a>). The
- type <tt>PositionMap</tt> must be a model of <a
- href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property
- Map</a> such that the vertex descriptor type of <tt>Graph</tt> is
- convertible to its key type. Its value type must be
- <tt>Topology::point_type</tt>, representing the coordinates
- of the vertex.<br>
- <b>Python</b>: The position map must be a <tt>vertex_point2d_map</tt> for
- the graph.<br>
- <b>Python default</b>: <tt>graph.get_vertex_point2d_map("position")</tt>
- </blockquote>
- IN: <tt>const Topology& space</tt>
- <blockquote>
- The topology used to lay out the vertices. This parameter describes both the
- size and shape of the layout area. Topologies are described in more detail
- (with a list of BGL-provided topologies) <a href="topology.html">in separate
- documentation</a>.
- </blockquote>
- <h3>Named Parameters</h3>
- IN: <tt>attractive_force(AttractiveForce fa)</tt>
- <blockquote>
- Computes the magnitude of the attractive force between two adjacent
- vertices. The function object <tt>fa</tt> must accept four
- parameters: the edge descriptor, <tt>k</tt>, the distance between the
- vertices, and the graph. <tt>k</tt> is the square root of the ratio
- of the display area to the number of vertices. <br>
- <b>Default:</b> <tt>square_distance_attractive_force()</tt>, which
- computes the attractive force as <code>dist<sup>2</sup>/k</code>.<br>
- <b>Python</b>: Any callable Python object that matches the signature will suffice.
- </blockquote>
- IN: <tt>repulsive_force(RepulsiveForce fr)</tt>
- <blockquote>
- Computes the magnitude of the repulsive force between any two
- vertices. The function object <tt>fr</tt> must accept five
- parameters: the two vertex descriptors, <tt>k</tt>, the distance between the
- vertices, and the graph. <tt>k</tt> is the square root of the ratio
- of the display area to the number of vertices. <br>
- <b>Default:</b> <tt>square_distance_repsulsive_force()</tt>, which
- computes the repulsive force as <code>k<sup>2</sup>/dist</code>.<br>
- <b>Python</b>: Any callable Python object that matches the signature will suffice.
- </blockquote>
- IN: <tt>force_pairs(ForcePairs fp)</tt>
- <blockquote>
- Enumerates the pairs of vertices on which the repulsive force should
- be applied. <tt>fp</tt> is a function object taking two parameters:
- the graph <tt>g</tt> and a binary function object that should be
- passed each pair of vertices to be considered. The basic formulation
- of the Fruchterman-Reingold algorithm computes repulsive forces
- between all pairs of vertices (pass <tt>all_force_pairs()</tt> for
- this parameter), which is functional for disconnected graphs but
- tends to push the connected components toward the edges of the
- display area. The grid variant of the algorithm places a grid over
- the display area and only computes repulsive forces among vertices
- within each rectangle in the grid. The grid variant can be more
- efficient than the basic formulation and tends to produce better
- layouts for disconnected graphs, but is not better overall: pass
- <tt>make_grid_force_pairs(width, height, position, g)</tt> as this
- parameter to use the grid variant. Other enumeration strategies may
- yield better results for particular graphs. <br>
- <b>Default:</b> <tt>make_grid_force_pairs(width, height, position, g)</tt><br>
- <b>Python</b>: Unsupported parameter.
- </blockquote>
- IN: <tt>cooling(Cooling cool)</tt>
- <blockquote>
- Determines the cooling schedule for the algorithm, which affects the
- rate of movement of vertices and termination of the algorithm. The
- <tt>cool</tt> parameter is a nullary function object (i.e., one that
- takes no arguments) and returns the temperature for the current
- iteration. When the returned temperature is zero, the algorithm
- terminates. Cooling schedules should begin with some initial
- temperature and gradually reduce the temperature to zero.<br>
- <b>Default:</b> <tt>linear_cooling<double>(100)</tt><br>
- <b>Python</b>: Any callable Python object that matches the signature will suffice.
- </blockquote>
- UTIL: <tt>displacement_map(DisplacementMap displacement)</tt>
- <blockquote>
- The displacement map is used to compute the amount by which each
- vertex will move in each step. The <tt>DisplacementMap</tt> type must be a
- property map whose key type is the graph's vertex type and whose value type is
- <tt>Topology::point_difference_type</tt>.<br>
- <b>Default:</b> An <tt>iterator_property_map</tt> with the specified value type
- and using the given vertex 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 is only necessary when no
- displacement map is provided.
- 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>adjacency_list</tt> with <tt>VertexList=listS</tt> does
- not have an internal <tt>vertex_index</tt> property.
- <br>
- <b>Python:</b> Unsupported parameter.
- </blockquote>
- <b>Python</b> IN: <tt>bool progressive</tt>
- <blockquote>
- When <tt>false</tt>, performs a random layout of the graph before
- running the Fruchterman-Reingold algorithm. If <tt>true</tt>, the
- algorithm is executing starting with the vertex configuration in
- the <tt>position</tt> map.<br>
- <b>Default</b>: <tt>False</tt>.
- </blockquote>
- <H3>Complexity</H3>
- <P> The time complexity is <i>O(|V|<sup>2</sup> + |E|)</i> for each
- iteration of the algorithm in the worst case. The average case for the
- grid variant is <i>O(|V| + |E|)</i>. The number of iterations is
- determined by the cooling schedule.
- <H3>Example</H3>
- <a href="../example/fr_layout.cpp">libs/graph/example/fr_layout.cpp</a>
- <br>
- <HR>
- <TABLE>
- <TR valign=top>
- <TD nowrap>Copyright © 2004, 2010 Trustees of Indiana University</TD><TD>
- <A HREF="http://www.boost.org/people/doug_gregor.html">Doug Gregor</A>, Indiana University
- </TD></TR></TABLE>
- </BODY>
- </HTML>
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