Boost Graph Library: Fruchterman-Reingold Force-Directed Layout

`fruchterman_reingold_force_directed_layout`

    // named parameter version
    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);

    // non-named parameter version
    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);

This algorithm [58] performs layout of unweighted, undirected graphs. Unlike the Kamada-Kawai layout algorithm, this algorithm directly supports the layout of disconnected graphs (but see the `force_pairs` named parameter). It is a force-directed 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 temperature 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.

The vertices are often placed randomly prior to execution of this algorithm via `random_graph_layout`.

### Where Defined

`boost/graph/fruchterman_reingold.hpp`

### Parameters

IN: `const Graph& g`

> The graph object on which the algorithm will be applied. The type `Graph` must be a model of Vertex And Edge List Graph.
> Python: This parameter is named `graph` in Python.

IN/OUT: `PositionMap position`

> The property map that stores the position of each vertex. It should typically be initialized with the vertices at random locations (use `random_graph_layout`). The type `PositionMap` must be a model of Lvalue Property Map such that the vertex descriptor type of `Graph` is convertible to its key type. Its value type must be `Topology::point_type`, representing the coordinates of the vertex.
> Python: The position map must be a `vertex_point2d_map` for the graph.
> Python default: `graph.get_vertex_point2d_map("position")`

IN: `const Topology& space`

> 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) in separate documentation.

### Named Parameters

IN: `attractive_force(AttractiveForce fa)`

> Computes the magnitude of the attractive force between two adjacent vertices. The function object `fa` must accept four parameters: the edge descriptor, `k`, the distance between the vertices, and the graph. `k` is the square root of the ratio of the display area to the number of vertices.
> Default: `square_distance_attractive_force()`, which computes the attractive force as `dist2/k`.
> Python: Any callable Python object that matches the signature will suffice.

IN: `repulsive_force(RepulsiveForce fr)`

> Computes the magnitude of the repulsive force between any two vertices. The function object `fa` must accept five parameters: the two vertex descriptors, `k`, the distance between the vertices, and the graph. `k` is the square root of the ratio of the display area to the number of vertices.
> Default: `square_distance_repsulsive_force()`, which computes the repulsive force as `k2/dist`.
> Python: Any callable Python object that matches the signature will suffice.

IN: `force_pairs(ForcePairs fp)`

> Enumerates the pairs of vertices on which the repulsive force should be applied. `fp` is a function object taking two parameters: the graph `g` 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 `all_force_pairs()` 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 `make_grid_force_pairs(width, height, position, g)` as this parameter to use the grid variant. Other enumeration strategies may yield better results for particular graphs.
> Default: `make_grid_force_pairs(width, height, position, g)`
> Python: Unsupported parameter.

IN: `cooling(Cooling cool)`

> Determines the cooling schedule for the algorithm, which affects the rate of movement of vertices and termination of the algorithm. The `cool` 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.
> Default: `linear_cooling<double>(100)`
> Python: Any callable Python object that matches the signature will suffice.

UTIL: `displacement_map(DisplacementMap displacement)`

> The displacement map is used to compute the amount by which each vertex will move in each step. The `DisplacementMap` type must be a property map whose key type is the graph's vertex type and whose value type is `Topology::point_difference_type`.
> Default: An `iterator_property_map` with the specified value type and using the given vertex index map.
> Python: Unsupported parameter.

IN: `vertex_index_map(VertexIndexMap i_map)`

> This maps each vertex to an integer in the range `[0, num_vertices(g))`. This is only necessary when no displacement map is provided. The type `VertexIndexMap` must be a model of Readable Property Map. 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.
> Default: `get(vertex_index, g)` Note: if you use this default, make sure your graph has an internal `vertex_index` property. For example, `adjacenty_list` with `VertexList=listS` does not have an internal `vertex_index` property.
> Python: Unsupported parameter.

Python IN: `bool progressive`

> When `false`, performs a random layout of the graph before running the Fruchterman-Reingold algorithm. If `true`, the algorithm is executing starting with the vertex configuration in the `position` map.
> Default: `False`.

### Complexity

The time complexity is O(|V|2 + |E|) for each iteration of the algorithm in the worse case. The average case for the grid variant is O(|V| + |E|). The number of iterations is determined by the cooling schedule.

### Example

libs/graph/example/fr_layout.cpp

Copyright © 2004, 2010 Trustees of Indiana University | Doug Gregor, Indiana University