Added boost header

test/external/boost/graph/kamada_kawai_spring_layout.hpp

@@ -0,0 +1,622 @@
+// Copyright 2004 The Trustees of Indiana University.
+
+// Distributed under the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+//  Authors: Douglas Gregor
+//           Andrew Lumsdaine
+#ifndef BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP
+#define BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP
+
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/topology.hpp>
+#include <boost/graph/iteration_macros.hpp>
+#include <boost/graph/johnson_all_pairs_shortest.hpp>
+#include <boost/type_traits/is_convertible.hpp>
+#include <utility>
+#include <iterator>
+#include <vector>
+#include <iostream>
+#include <boost/limits.hpp>
+#include <boost/config/no_tr1/cmath.hpp>
+
+namespace boost {
+  namespace detail { namespace graph {
+    /**
+     * Denotes an edge or display area side length used to scale a
+     * Kamada-Kawai drawing.
+     */
+    template<bool Edge, typename T>
+    struct edge_or_side
+    {
+      explicit edge_or_side(T value) : value(value) {}
+
+      T value;
+    };
+
+    /**
+     * Compute the edge length from an edge length. This is trivial.
+     */
+    template<typename Graph, typename DistanceMap, typename IndexMap, 
+             typename T>
+    T compute_edge_length(const Graph&, DistanceMap, IndexMap, 
+                          edge_or_side<true, T> length)
+    { return length.value; }
+
+    /**
+     * Compute the edge length based on the display area side
+       length. We do this by dividing the side length by the largest
+       shortest distance between any two vertices in the graph.
+     */
+    template<typename Graph, typename DistanceMap, typename IndexMap, 
+             typename T>
+    T
+    compute_edge_length(const Graph& g, DistanceMap distance, IndexMap index,
+                        edge_or_side<false, T> length)
+    {
+      T result(0);
+
+      typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
+
+      for (vertex_iterator ui = vertices(g).first, end = vertices(g).second;
+           ui != end; ++ui) {
+        vertex_iterator vi = ui;
+        for (++vi; vi != end; ++vi) {
+          T dij = distance[get(index, *ui)][get(index, *vi)];
+          if (dij > result) result = dij;
+        }
+      }
+      return length.value / result;
+    }
+
+    /**
+     * Dense linear solver for fixed-size matrices.
+     */
+    template <std::size_t Size>
+    struct linear_solver {
+      // Indices in mat are (row, column)
+      // template <typename Vec>
+      // static Vec solve(double mat[Size][Size], Vec rhs);
+    };
+
+    template <>
+    struct linear_solver<1> {
+      template <typename Vec>
+      static Vec solve(double mat[1][1], Vec rhs) {
+        return rhs / mat[0][0];
+      }
+    };
+
+    // These are from http://en.wikipedia.org/wiki/Cramer%27s_rule
+    template <>
+    struct linear_solver<2> {
+      template <typename Vec>
+      static Vec solve(double mat[2][2], Vec rhs) {
+        double denom = mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1];
+        double x_num = rhs[0]    * mat[1][1] - rhs[1]    * mat[0][1];
+        double y_num = mat[0][0] * rhs[1]    - mat[1][0] * rhs[0]   ;
+        Vec result;
+        result[0] = x_num / denom;
+        result[1] = y_num / denom;
+        return result;
+      }
+    };
+
+    template <>
+    struct linear_solver<3> {
+      template <typename Vec>
+      static Vec solve(double mat[2][2], Vec rhs) {
+        double denom = mat[0][0] * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
+                     - mat[1][0] * (mat[0][1] * mat[2][2] - mat[2][1] * mat[0][2])
+                     + mat[2][0] * (mat[0][1] * mat[1][2] - mat[1][1] * mat[0][2]);
+        double x_num = rhs[0]    * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
+                     - rhs[1]    * (mat[0][1] * mat[2][2] - mat[2][1] * mat[0][2])
+                     + rhs[2]    * (mat[0][1] * mat[1][2] - mat[1][1] * mat[0][2]);
+        double y_num = mat[0][0] * (rhs[1]    * mat[2][2] - rhs[2]    * mat[1][2])
+                     - mat[1][0] * (rhs[0]    * mat[2][2] - rhs[2]    * mat[0][2])
+                     + mat[2][0] * (rhs[0]    * mat[1][2] - rhs[1]    * mat[0][2]);
+        double z_num = mat[0][0] * (mat[1][1] * rhs[2]    - mat[2][1] * rhs[1]   )
+                     - mat[1][0] * (mat[0][1] * rhs[2]    - mat[2][1] * rhs[0]   )
+                     + mat[2][0] * (mat[0][1] * rhs[1]    - mat[1][1] * rhs[0]   );
+        Vec result;
+        result[0] = x_num / denom;
+        result[1] = y_num / denom;
+        result[2] = z_num / denom;
+        return result;
+      }
+    };
+
+    /**
+     * Implementation of the Kamada-Kawai spring layout algorithm.
+     */
+    template<typename Topology, typename Graph, typename PositionMap, typename WeightMap,
+             typename EdgeOrSideLength, typename Done,
+             typename VertexIndexMap, typename DistanceMatrix,
+             typename SpringStrengthMatrix, typename PartialDerivativeMap>
+    struct kamada_kawai_spring_layout_impl
+    {
+      typedef typename property_traits<WeightMap>::value_type weight_type;
+      typedef typename Topology::point_type Point;
+      typedef typename Topology::point_difference_type point_difference_type;
+      typedef point_difference_type deriv_type;
+      typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
+      typedef typename graph_traits<Graph>::vertex_descriptor
+        vertex_descriptor;
+
+      kamada_kawai_spring_layout_impl(
+        const Topology& topology,
+        const Graph& g, 
+        PositionMap position,
+        WeightMap weight, 
+        EdgeOrSideLength edge_or_side_length,
+        Done done,
+        weight_type spring_constant,
+        VertexIndexMap index,
+        DistanceMatrix distance,
+        SpringStrengthMatrix spring_strength,
+        PartialDerivativeMap partial_derivatives)
+        : topology(topology), g(g), position(position), weight(weight), 
+          edge_or_side_length(edge_or_side_length), done(done),
+          spring_constant(spring_constant), index(index), distance(distance),
+          spring_strength(spring_strength), 
+          partial_derivatives(partial_derivatives) {}
+
+      // Compute contribution of vertex i to the first partial
+      // derivatives (dE/dx_m, dE/dy_m) (for vertex m)
+      deriv_type
+      compute_partial_derivative(vertex_descriptor m, vertex_descriptor i)
+      {
+#ifndef BOOST_NO_STDC_NAMESPACE
+        using std::sqrt;
+#endif // BOOST_NO_STDC_NAMESPACE
+
+        deriv_type result;
+        if (i != m) {
+          point_difference_type diff = topology.difference(position[m], position[i]);
+          weight_type dist = topology.norm(diff);
+          result = spring_strength[get(index, m)][get(index, i)] 
+            * (diff - distance[get(index, m)][get(index, i)]/dist*diff);
+        }
+
+        return result;
+      }
+
+      // Compute partial derivatives dE/dx_m and dE/dy_m
+      deriv_type 
+      compute_partial_derivatives(vertex_descriptor m)
+      {
+#ifndef BOOST_NO_STDC_NAMESPACE
+        using std::sqrt;
+#endif // BOOST_NO_STDC_NAMESPACE
+
+        deriv_type result;
+
+        // TBD: looks like an accumulate to me
+        BGL_FORALL_VERTICES_T(i, g, Graph) {
+          deriv_type deriv = compute_partial_derivative(m, i);
+          result += deriv;
+        }
+
+        return result;
+      }
+
+      // The actual Kamada-Kawai spring layout algorithm implementation
+      bool run()
+      {
+#ifndef BOOST_NO_STDC_NAMESPACE
+        using std::sqrt;
+#endif // BOOST_NO_STDC_NAMESPACE
+
+        // Compute d_{ij} and place it in the distance matrix
+        if (!johnson_all_pairs_shortest_paths(g, distance, index, weight, 
+                                              weight_type(0)))
+          return false;
+
+        // Compute L based on side length (if needed), or retrieve L
+        weight_type edge_length = 
+          detail::graph::compute_edge_length(g, distance, index,
+                                             edge_or_side_length);
+
+        std::cerr << "edge_length = " << edge_length << std::endl;
+        
+        // Compute l_{ij} and k_{ij}
+        const weight_type K = spring_constant;
+        vertex_iterator ui, end;
+        for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+          vertex_iterator vi = ui;
+          for (++vi; vi != end; ++vi) {
+            weight_type dij = distance[get(index, *ui)][get(index, *vi)];
+            if (dij == (std::numeric_limits<weight_type>::max)())
+              return false;
+            distance[get(index, *ui)][get(index, *vi)] = edge_length * dij;
+            distance[get(index, *vi)][get(index, *ui)] = edge_length * dij;
+            spring_strength[get(index, *ui)][get(index, *vi)] = K/(dij*dij);
+            spring_strength[get(index, *vi)][get(index, *ui)] = K/(dij*dij);
+          }
+        }
+        
+        // Compute Delta_i and find max
+        vertex_descriptor p = *vertices(g).first;
+        weight_type delta_p(0);
+
+        for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+          deriv_type deriv = compute_partial_derivatives(*ui);
+          put(partial_derivatives, *ui, deriv);
+
+          weight_type delta = topology.norm(deriv);
+
+          if (delta > delta_p) {
+            p = *ui;
+            delta_p = delta;
+          }
+        }
+
+        while (!done(delta_p, p, g, true)) {
+          // The contribution p makes to the partial derivatives of
+          // each vertex. Computing this (at O(n) cost) allows us to
+          // update the delta_i values in O(n) time instead of O(n^2)
+          // time.
+          std::vector<deriv_type> p_partials(num_vertices(g));
+          for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+            vertex_descriptor i = *ui;
+            p_partials[get(index, i)] = compute_partial_derivative(i, p);
+          }
+
+          do {
+            // For debugging, compute the energy value E
+            double E = 0.;
+            for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+              vertex_iterator vi = ui;
+              for (++vi; vi != end; ++vi) {
+                double dist = topology.distance(position[*ui], position[*vi]);
+                weight_type k_ij = spring_strength[get(index,*ui)][get(index,*vi)];
+                weight_type l_ij = distance[get(index, *ui)][get(index, *vi)];
+                E += .5 * k_ij * (dist - l_ij) * (dist - l_ij);
+              }
+            }
+            std::cerr << "E = " << E << std::endl;
+
+            // Compute the elements of the Jacobian
+            // From
+            // http://www.cs.panam.edu/~rfowler/papers/1994_kumar_fowler_A_Spring_UTPACSTR.pdf
+            // with the bugs fixed in the off-diagonal case
+            weight_type dE_d_d[Point::dimensions][Point::dimensions];
+            for (std::size_t i = 0; i < Point::dimensions; ++i)
+              for (std::size_t j = 0; j < Point::dimensions; ++j)
+                dE_d_d[i][j] = 0.;
+            for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+              vertex_descriptor i = *ui;
+              if (i != p) {
+                point_difference_type diff = topology.difference(position[p], position[i]);
+                weight_type dist = topology.norm(diff);
+                weight_type dist_squared = dist * dist;
+                weight_type inv_dist_cubed = 1. / (dist_squared * dist);
+                weight_type k_mi = spring_strength[get(index,p)][get(index,i)];
+                weight_type l_mi = distance[get(index, p)][get(index, i)];
+                for (std::size_t i = 0; i < Point::dimensions; ++i) {
+                  for (std::size_t j = 0; j < Point::dimensions; ++j) {
+                    if (i == j) {
+                      dE_d_d[i][i] += k_mi * (1 + (l_mi * (diff[i] * diff[i] - dist_squared) * inv_dist_cubed));
+                    } else {
+                      dE_d_d[i][j] += k_mi * l_mi * diff[i] * diff[j] * inv_dist_cubed;
+                      // dE_d_d[i][j] += k_mi * l_mi * sqrt(hypot(diff[i], diff[j])) * inv_dist_cubed;
+                    }
+                  }
+                }
+              }
+            }
+
+            deriv_type dE_d = get(partial_derivatives, p);
+
+            // Solve dE_d_d * delta = -dE_d to get delta
+            point_difference_type delta = -linear_solver<Point::dimensions>::solve(dE_d_d, dE_d);
+
+            // Move p by delta
+            position[p] = topology.adjust(position[p], delta);
+
+            // Recompute partial derivatives and delta_p
+            deriv_type deriv = compute_partial_derivatives(p);
+            put(partial_derivatives, p, deriv);
+
+            delta_p = topology.norm(deriv);
+          } while (!done(delta_p, p, g, false));
+
+          // Select new p by updating each partial derivative and delta
+          vertex_descriptor old_p = p;
+          for (ui = vertices(g).first, end = vertices(g).second; ui != end; ++ui) {
+            deriv_type old_deriv_p = p_partials[get(index, *ui)];
+            deriv_type old_p_partial = 
+              compute_partial_derivative(*ui, old_p);
+            deriv_type deriv = get(partial_derivatives, *ui);
+
+            deriv += old_p_partial - old_deriv_p;
+
+            put(partial_derivatives, *ui, deriv);
+            weight_type delta = topology.norm(deriv);
+
+            if (delta > delta_p) {
+              p = *ui;
+              delta_p = delta;
+            }
+          }
+        }
+
+        return true;
+      }
+
+      const Topology& topology;
+      const Graph& g; 
+      PositionMap position;
+      WeightMap weight; 
+      EdgeOrSideLength edge_or_side_length;
+      Done done;
+      weight_type spring_constant;
+      VertexIndexMap index;
+      DistanceMatrix distance;
+      SpringStrengthMatrix spring_strength;
+      PartialDerivativeMap partial_derivatives;
+    };
+  } } // end namespace detail::graph
+
+  /// States that the given quantity is an edge length.
+  template<typename T> 
+  inline detail::graph::edge_or_side<true, T>
+  edge_length(T x) 
+  { return detail::graph::edge_or_side<true, T>(x); }
+
+  /// States that the given quantity is a display area side length.
+  template<typename T> 
+  inline detail::graph::edge_or_side<false, T>
+  side_length(T x) 
+  { return detail::graph::edge_or_side<false, T>(x); }
+
+  /** 
+   * \brief Determines when to terminate layout of a particular graph based
+   * on a given relative tolerance. 
+   */
+  template<typename T = double>
+  struct layout_tolerance
+  {
+    layout_tolerance(const T& tolerance = T(0.001))
+      : tolerance(tolerance), last_energy((std::numeric_limits<T>::max)()),
+        last_local_energy((std::numeric_limits<T>::max)()) { }
+
+    template<typename Graph>
+    bool 
+    operator()(T delta_p, 
+               typename boost::graph_traits<Graph>::vertex_descriptor p,
+               const Graph& g,
+               bool global)
+    {
+      if (global) {
+        if (last_energy == (std::numeric_limits<T>::max)()) {
+          last_energy = delta_p;
+          return false;
+        }
+          
+        T diff = last_energy - delta_p;
+        if (diff < T(0)) diff = -diff;
+        bool done = (delta_p == T(0) || diff / last_energy < tolerance);
+        last_energy = delta_p;
+        return done;
+      } else {
+        if (last_local_energy == (std::numeric_limits<T>::max)()) {
+          last_local_energy = delta_p;
+          return delta_p == T(0);
+        }
+          
+        T diff = last_local_energy - delta_p;
+        bool done = (delta_p == T(0) || (diff / last_local_energy) < tolerance);
+        last_local_energy = delta_p;
+        return done;
+      }
+    }
+
+  private:
+    T tolerance;
+    T last_energy;
+    T last_local_energy;
+  };
+
+  /** \brief Kamada-Kawai spring layout for undirected graphs.
+   *
+   * This algorithm 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.
+   *
+   * \param g (IN) must be a model of Vertex List Graph, Edge List
+   * Graph, and Incidence Graph and must be undirected.
+   *
+   * \param position (OUT) must be a model of Lvalue Property Map,
+   * where the value type is a class containing fields @c x and @c y
+   * that will be set to the @c x and @c y coordinates of each vertex.
+   *
+   * \param weight (IN) must be a model of Readable Property Map,
+   * which provides the weight of each edge in the graph @p g.
+   *
+   * \param topology (IN) must be a topology object (see topology.hpp),
+   * which provides operations on points and differences between them.
+   *
+   * \param edge_or_side_length (IN) provides either the unit length
+   * @c e of an edge in the layout or the length of a side @c s of the
+   * display area, and must be either @c boost::edge_length(e) or @c
+   * boost::side_length(s), respectively.
+   *
+   * \param done (IN) is a 4-argument function object that is passed
+   * the current value of delta_p (i.e., the energy of vertex @p p),
+   * the vertex @p p, the graph @p g, and a boolean flag indicating
+   * whether @p delta_p is the maximum energy in the system (when @c
+   * true) or the energy of the vertex being moved. Defaults to @c
+   * layout_tolerance instantiated over the value type of the weight
+   * map.
+   *
+   * \param spring_constant (IN) is 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. The default value is 1.
+   *
+   * \param index (IN) is a mapping from vertices to index values
+   * between 0 and @c num_vertices(g). The default is @c
+   * get(vertex_index,g).
+   *
+   * \param distance (UTIL/OUT) 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. The default is a a vector of vectors.
+   *
+   * \param spring_strength (UTIL/OUT) 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. The default is a a vector of
+   * vectors.
+   *
+   * \param partial_derivatives (UTIL) will be used to store the
+   * partial derivates of each vertex with respect to the @c x and @c
+   * y coordinates. This must be a Read/Write Property Map whose value
+   * type is a pair with both types equivalent to the value type of
+   * the weight map. The default is an iterator property map.
+   *
+   * \returns @c true if layout was successful or @c false if a
+   * negative weight cycle was detected.
+   */
+  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& topology,
+    detail::graph::edge_or_side<EdgeOrSideLength, T> edge_or_side_length,
+    Done done,
+    typename property_traits<WeightMap>::value_type spring_constant,
+    VertexIndexMap index,
+    DistanceMatrix distance,
+    SpringStrengthMatrix spring_strength,
+    PartialDerivativeMap partial_derivatives)
+  {
+    BOOST_STATIC_ASSERT((is_convertible<
+                           typename graph_traits<Graph>::directed_category*,
+                           undirected_tag*
+                         >::value));
+
+    detail::graph::kamada_kawai_spring_layout_impl<
+      Topology, Graph, PositionMap, WeightMap, 
+      detail::graph::edge_or_side<EdgeOrSideLength, T>, Done, VertexIndexMap, 
+      DistanceMatrix, SpringStrengthMatrix, PartialDerivativeMap>
+      alg(topology, g, position, weight, edge_or_side_length, done, spring_constant,
+          index, distance, spring_strength, partial_derivatives);
+    return alg.run();
+  }
+
+  /**
+   * \overload
+   */
+  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& topology,
+    detail::graph::edge_or_side<EdgeOrSideLength, T> edge_or_side_length,
+    Done done,
+    typename property_traits<WeightMap>::value_type spring_constant,
+    VertexIndexMap index)
+  {
+    typedef typename property_traits<WeightMap>::value_type weight_type;
+
+    typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
+    typedef std::vector<weight_type> weight_vec;
+
+    std::vector<weight_vec> distance(n, weight_vec(n));
+    std::vector<weight_vec> spring_strength(n, weight_vec(n));
+    std::vector<typename Topology::point_difference_type> partial_derivatives(n);
+
+    return 
+      kamada_kawai_spring_layout(
+        g, position, weight, topology, edge_or_side_length, done, spring_constant, index,
+        distance.begin(),
+        spring_strength.begin(),
+        make_iterator_property_map(partial_derivatives.begin(), index,
+                                   typename Topology::point_difference_type()));
+  }
+
+  /**
+   * \overload
+   */
+  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& topology,
+    detail::graph::edge_or_side<EdgeOrSideLength, T> edge_or_side_length,
+    Done done,
+    typename property_traits<WeightMap>::value_type spring_constant)
+  {
+    return kamada_kawai_spring_layout(g, position, weight, topology, edge_or_side_length,
+                                      done, spring_constant, 
+                                      get(vertex_index, g));
+  }
+
+  /**
+   * \overload
+   */
+  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& topology,
+    detail::graph::edge_or_side<EdgeOrSideLength, T> edge_or_side_length,
+    Done done)
+  {
+    typedef typename property_traits<WeightMap>::value_type weight_type;
+    return kamada_kawai_spring_layout(g, position, weight, topology, edge_or_side_length,
+                                      done, weight_type(1)); 
+  }
+
+  /**
+   * \overload
+   */
+  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& topology,
+    detail::graph::edge_or_side<EdgeOrSideLength, T> edge_or_side_length)
+  {
+    typedef typename property_traits<WeightMap>::value_type weight_type;
+    return kamada_kawai_spring_layout(g, position, weight, topology, edge_or_side_length,
+                                      layout_tolerance<weight_type>(),
+                                      weight_type(1.0), 
+                                      get(vertex_index, g));
+  }
+} // end namespace boost
+
+#endif // BOOST_GRAPH_KAMADA_KAWAI_SPRING_LAYOUT_HPP