`kamada_kawai_spring_layout`

Kamada-Kawai spring layout for connected, undirected graphs.

Defined in: <boost/graph/kamada_kawai_spring_layout.hpp>

Example

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/kamada_kawai_spring_layout.hpp>
#include <boost/graph/circle_layout.hpp>
#include <boost/graph/topology.hpp>
#include <iostream>
#include <vector>
#include <iomanip>

struct Spring { double length; };

int main() {
    using namespace boost;
    using Graph = adjacency_list<vecS, vecS, undirectedS, no_property, Spring>;

    Graph g(5);
    add_edge(0, 1, Spring{1.0}, g);
    add_edge(1, 2, Spring{1.0}, g);
    add_edge(2, 3, Spring{1.0}, g);
    add_edge(3, 4, Spring{1.0}, g);
    add_edge(4, 0, Spring{1.0}, g);

    using Topo = rectangle_topology<>;
    Topo topo(0.0, 0.0, 100.0, 100.0);
    using Point = Topo::point_type;

    std::vector<Point> pos(num_vertices(g));
    auto pos_map = make_iterator_property_map(pos.begin(), get(vertex_index, g));

    circle_graph_layout(g, pos_map, 25.0);

    // Bundled spring-length via member pointer — no edge_weight_t tag needed.
    bool ok = kamada_kawai_spring_layout(g, pos_map, get(&Spring::length, g),
        topo, side_length(50.0), layout_tolerance<double>(0.1));

    std::cout << std::fixed << std::setprecision(1);
    std::cout << "converged: " << (ok ? "yes" : "no") << "\n";
    for (auto v : make_iterator_range(vertices(g))) {
        std::cout << "vertex " << v << ": ("
                  << pos[v][0] << ", " << pos[v][1] << ")\n";
    }
}

converged: yes
vertex 0: (21.7, -0.0)
vertex 1: (7.7, 23.8)
vertex 2: (-20.2, 14.7)
vertex 3: (-20.2, -14.7)
vertex 4: (5.8, -22.0)

(1) Full version

template<typename Topology, typename Graph, typename PositionMap,
         typename WeightMap, typename T, bool EdgeOrSideLength,
         typename Done, typename VertexIndexMap,
         typename DistanceMatrix, typename SpringStrengthMatrix,
         typename PartialDerivativeMap>
bool kamada_kawai_spring_layout(
    const Graph& g,
    PositionMap position,
    WeightMap weight,
    const Topology& space,
    unspecified edge_or_side_length,
    Done done,
    typename property_traits<WeightMap>::value_type spring_constant,
    VertexIndexMap index,
    DistanceMatrix distance,
    SpringStrengthMatrix spring_strength,
    PartialDerivativeMap partial_derivatives);

Direction Parameter Description

Direction	Parameter	Description
IN	`const Graph& g`	The graph, whose type `Graph` must model the VertexListGraph, EdgeListGraph, and IncidenceGraph concepts. The graph must be undirected and connected.
OUT	`PositionMap position`	This property map is used to store the position of each vertex. The type `PositionMap` must be a model of Writable Property Map, with the graph’s vertex descriptor type as its key type and `Topology::point_type` as its value type.
IN	`WeightMap weight`	The weight or "length" of each edge in the graph. The weights must all be non-negative, and the algorithm will throw a `negative_edge` exception if one of the edges is negative. The type `WeightMap` must be a model of Readable Property Map. The edge descriptor type of the graph needs to be usable as the key type for the weight map. The value type for this map must be the same as the value type of the distance map. Default: `get(edge_weight, g)`
IN	`const Topology& space`	The topology used to lay out the vertices. This parameter describes both the size and shape of the layout area, as well as its dimensionality; up to three dimensions are supported by the current implementation. Topologies are described in more detail (with a list of BGL-provided topologies) in separate documentation.
IN	`unspecified edge_or_side_length`	Provides either the unit length `e` of an edge in the layout or the length of a side `s` of the display area, and must be either `boost::edge_length(e)` or `boost::side_length(s)`, respectively.
IN	`Done done`	A 4-argument function object that is passed the current value of delta_p (i.e., the energy of vertex `p`), the vertex `p`, the graph `g`, and a boolean flag indicating whether `delta_p` is the maximum energy in the system (when `true`) or the energy of the vertex being moved. Default: `layout_tolerance` instantiated over the value type of the weight map.
IN	`typename property_traits<WeightMap>::value_type spring_constant`	The constant multiplied by each spring’s strength. Larger values create systems with more energy that can take longer to stabilize; smaller values create systems with less energy that stabilize quickly but do not necessarily result in pleasing layouts. Default: 1.
IN	`VertexIndexMap index`	A mapping from vertices to index values between 0 and `num_vertices(g)`. Default: `get(vertex_index,g)`. Note: if you use this default, make sure your graph has an internal `vertex_index` property. For example, `adjacency_list` with `VertexList=listS` does not have an internal `vertex_index` property.
UTIL/OUT	`DistanceMatrix distance`	This parameter will be used to store the distance from every vertex to every other vertex, which is computed in the first stages of the algorithm. This value’s type must be a model of `BasicMatrix` with value type equal to the value type of the weight map. Default: A vector of vectors.
UTIL/OUT	`SpringStrengthMatrix spring_strength`	This matrix will be used to store the strength of the spring between every pair of vertices. This value’s type must be a model of BasicMatrix with value type equal to the value type of the weight map. Default: A vector of vectors of the value type of the weight map.
UTIL	`PartialDerivativeMap partial_derivatives`	A property map that will be used to store the partial derivatives of each vertex with respect to the vertex’s current coordinates. This must be a Read/Write Property Map whose value type is `Topology::point_difference_type`. The default is an iterator property map built using the graph’s vertex index map. Default: An `iterator_property_map` created from an `std::vector` of `Topology::point_difference_type`.

const Graph& g

The graph, whose type Graph must model the VertexListGraph, EdgeListGraph, and IncidenceGraph concepts. The graph must be undirected and connected.

OUT

PositionMap position

This property map is used to store the position of each vertex. The type PositionMap must be a model of Writable Property Map, with the graph’s vertex descriptor type as its key type and Topology::point_type as its value type.

WeightMap weight

The weight or "length" of each edge in the graph. The weights must all be non-negative, and the algorithm will throw a negative_edge exception if one of the edges is negative. The type WeightMap must be a model of Readable Property Map. The edge descriptor type of the graph needs to be usable as the key type for the weight map. The value type for this map must be the same as the value type of the distance map.
Default: get(edge_weight, g)

const Topology& space

The topology used to lay out the vertices. This parameter describes both the size and shape of the layout area, as well as its dimensionality; up to three dimensions are supported by the current implementation. Topologies are described in more detail (with a list of BGL-provided topologies) in separate documentation.

unspecified edge_or_side_length

Provides either the unit length e of an edge in the layout or the length of a side s of the display area, and must be either boost::edge_length(e) or boost::side_length(s), respectively.

Done done

A 4-argument function object that is passed the current value of delta_p (i.e., the energy of vertex p), the vertex p, the graph g, and a boolean flag indicating whether delta_p is the maximum energy in the system (when true) or the energy of the vertex being moved.
Default: layout_tolerance instantiated over the value type of the weight map.

typename property_traits<WeightMap>::value_type spring_constant

The constant multiplied by each spring’s strength. Larger values create systems with more energy that can take longer to stabilize; smaller values create systems with less energy that stabilize quickly but do not necessarily result in pleasing layouts.
Default: 1.

VertexIndexMap index

A mapping from vertices to index values between 0 and num_vertices(g).
Default: get(vertex_index,g). Note: if you use this default, make sure your graph has an internal vertex_index property. For example, adjacency_list with VertexList=listS does not have an internal vertex_index property.

UTIL/OUT

DistanceMatrix distance

This parameter will be used to store the distance from every vertex to every other vertex, which is computed in the first stages of the algorithm. This value’s type must be a model of BasicMatrix with value type equal to the value type of the weight map.
Default: A vector of vectors.

UTIL/OUT

SpringStrengthMatrix spring_strength

This matrix will be used to store the strength of the spring between every pair of vertices. This value’s type must be a model of BasicMatrix with value type equal to the value type of the weight map.
Default: A vector of vectors of the value type of the weight map.

UTIL

PartialDerivativeMap partial_derivatives

A property map that will be used to store the partial derivatives of each vertex with respect to the vertex’s current coordinates. This must be a Read/Write Property Map whose value type is Topology::point_difference_type. The default is an iterator property map built using the graph’s vertex index map.
Default: An iterator_property_map created from an std::vector of Topology::point_difference_type.

(2) Without utility maps

template<typename Topology, typename Graph, typename PositionMap,
         typename WeightMap, typename T, bool EdgeOrSideLength,
         typename Done, typename VertexIndexMap>
bool kamada_kawai_spring_layout(
    const Graph& g,
    PositionMap position,
    WeightMap weight,
    const Topology& space,
    unspecified edge_or_side_length,
    Done done,
    typename property_traits<WeightMap>::value_type spring_constant,
    VertexIndexMap index);

Same parameters as (1), but without the distance, spring_strength, and partial_derivatives utility maps, which will be created internally.

(3) With default spring constant

template<typename Topology, typename Graph, typename PositionMap,
         typename WeightMap, typename T, bool EdgeOrSideLength,
         typename Done>
bool kamada_kawai_spring_layout(
    const Graph& g,
    PositionMap position,
    WeightMap weight,
    const Topology& space,
    unspecified edge_or_side_length,
    Done done,
    typename property_traits<WeightMap>::value_type spring_constant =
        typename property_traits<WeightMap>::value_type(1));

Same parameters as (2), but uses a default vertex index map of get(vertex_index, g).

(4) Minimal version

template<typename Topology, typename Graph, typename PositionMap,
         typename WeightMap, typename T, bool EdgeOrSideLength>
bool kamada_kawai_spring_layout(
    const Graph& g,
    PositionMap position,
    WeightMap weight,
    const Topology& space,
    unspecified edge_or_side_length);

Same parameters as (3), but uses a default done function of layout_tolerance instantiated over the value type of the weight map and a default spring constant of 1.

Description

This algorithm [52] performs graph layout (in two dimensions) for connected, undirected graphs. It operates by relating the layout of graphs to a dynamic spring system and minimizing the energy within that system. The strength of a spring between two vertices is inversely proportional to the square of the shortest distance (in graph terms) between those two vertices. Essentially, vertices that are closer in the graph-theoretic sense (i.e., by following edges) will have stronger springs and will therefore be placed closer together.

Prior to invoking this algorithm, it is recommended that the vertices be placed along the vertices of a regular n-sided polygon via circle_graph_layout.

Returns

true if layout was successful or false if a negative weight cycle was detected or the graph is disconnected.

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