Mauch MIREX 2010

function [jtree, root, cliques, B, w, elim_order] = graph_to_jtree(MG, ns, partial_order, stages, clusters)

% GRAPH_TO_JTREE Triangulate a graph and make a junction tree from its cliques.

% [jtree, root, cliques, B, w, elim_order] = ...

%    graph_to_jtree(graph, node_sizes, partial_order, stages, clusters)

%

% INPUT:

% graph(i,j) = 1 iff there is an edge between i,j

% node_weights(i) = num discrete values node i can take on [1 if observed]

% partial_order = {} if no constraints on elimination ordering

% stages{i} = nodes that must be eliminated at i'th stage (if porder is empty)

% clusters{i} = list of nodes that must get connected together in the moral graph

%

% OUTPUT:

% jtree(i,j) = 1 iff there is an arc between clique i and clique j 

% root = the root clique

% cliques{i} = the nodes in clique i

% B(i,j) = 1 iff node j occurs in clique i

% w(i) = weight of clique i

N = length(MG);

if nargin >= 5

  % Add extra arcs between nodes in each cluster to ensure they occur in the same clique

  for i=1:length(clusters)

    c = clusters{i};

    MG(c,c) = 1;

  end

end

MG = setdiag(MG, 0);

% Find an optimal elimination ordering (NP-hard problem!)

if nargin < 4

  stages = {1:N};

end

if nargin < 3

  partial_order = {};

end

if isempty(partial_order)

  strong = 0;

  elim_order = best_first_elim_order(MG, ns, stages);

else

  strong = 1;

  elim_order = strong_elim_order(MG, ns, partial_order);

end

[MTG, cliques, fill_in_edges]  = triangulate(MG, elim_order);

% Connect the cliques up into a jtree,

[jtree, root, B, w] = cliques_to_jtree(cliques, ns);

if 0

  disp('testing dag to jtree');

  % Find the cliques containing each node, and check they form a connected subtree

  clqs_con_node = cell(1,N);

  for i=1:N

    clqs_con_node{i} = find(B(:,i))';

  end

  check_jtree_property(clqs_con_node, jtree);

end