minimum_degree_ordering

  template <class AdjacencyGraph, class OutDegreeMap,
           class InversePermutationMap, 
           class PermutationMap, class SuperNodeSizeMap, class VertexIndexMap>
  void minimum_degree_ordering
    (AdjacencyGraph& G,
     OutDegreeMap outdegree,
     InversePermutationMap inverse_perm,
     PermutationMap perm, 
     SuperNodeSizeMap supernode_size, int delta, VertexIndexMap id) 

The graph G corresponding to a symmetric matrix A should be directed one instead of a undirected graph in this implementation. Therefore, nonzero entry A(i, j) corresponds two directed edges (e(i,j) and e(j,i)) in G.

The output of the algorithm are the vertices in the new ordering.

  inverse_perm[new_index[u]] == old_index[u]

and the permutation from the old index to the new index.

  perm[old_index[u]] == new_index[u]

The following equations are always held.

  for (size_type i = 0; i != inverse_perm.size(); ++i)
    perm[inverse_perm[i]] == i;

Parameters

• AdjacencyGraph& G  (IN)
  A directed graph. The graph's type must be a model of Adjacency Graph, Vertex List Graph, and Mutable Incidence Graph. In addition, the functions num_vertices() and out_degree() are required.
• OutDegreeMap outdegree  (WORK)
  This is used internally to store the out degree of vertices. This must be a LvaluePropertyMap with key type the same as the vertex descriptor type of the graph, and with a value type that is an integer type.
• InversePermutationMap inverse_perm  (OUT)
  The new vertex ordering, given as the mapping from the new indices to the old indices (an inverse permutation). This must be an LvaluePropertyMap with a value type and key type a signed integer.
• PermutationMap perm  (OUT)
  The new vertex ordering, given as the mapping from the old indices to the new indices (a permutation). This must be an LvaluePropertyMap with a value type and key type a signed integer.
• SuperNodeSizeMap supernode_size  (WORK/OUT)
  This is used internally to record the size of supernodes and is also useful information to have. This is a LvaluePropertyMap with an unsigned integer value type and key type of vertex descriptor.
• int delta  (IN)
  Multiple elimination control variable. If it is larger than or equal to zero then multiple elimination is enabled. The value of delta specifies the difference between the minimum degree and the degree of vertices that are to be eliminated.
• VertexIndexMap id  (IN)
  Used internally to map vertices to their indices. This must be a Readable Property Map with key type the same as the vertex descriptor of the graph and a value type that is some unsigned integer type.