function clusterIdx = recursiveNCuts(anAffinityMat)
%Implementation of the recursive N-cuts algorithm
%   Usage clusters = recursiveNCuts (anAffinityMat), where:
%       Inputs
%       - anAffinityMat is a rectangular, symmetrical affinity matrix
%           representation of an image
%       Output
%       - clusterIdx is a vector storing the cluster Id of each node

    % Makes sure preconditions are met
    if ~issymmetric(anAffinityMat)
        error('The affinity matrix provided is not symmetric.');
    end

    % Executes clustering using N-Cuts algorithm
    clusterIdx = myNCuts(anAffinityMat, 2);
    
    % Checks stop conditions
    if (nnz(clusterIdx == 1) < 5 || nnz(clusterIdx == 2) < 5)
        clusterIdx = [];
        return;
    end
    NCut = calculateNcut(anAffinityMat, clusterIdx);
    if (NCut > 0.2)
        clusterIdx = [];
        return;
    end
    
    % Finds indices of each cluster
    clusterOneIndices = (clusterIdx == 1);
    clusterTwoIndices = (clusterIdx == 2);
    
    % Recursively calls itself for each part of the matrix
    firstSubClusters = recursiveNCuts(anAffinityMat(clusterOneIndices, ...
        clusterOneIndices));
    secondSubClusters = recursiveNCuts(anAffinityMat(clusterTwoIndices, ...
        clusterTwoIndices));
    
    % Re-merges the sub-cluster arrays
    if ~isempty(firstSubClusters)
        clusterIdx(clusterOneIndices) = firstSubClusters;
    end    
    if ~isempty(secondSubClusters)
        clusterIdx(clusterTwoIndices) = secondSubClusters;
    end
    
    % Makes sure the IDs of the clusters of each half are unique
    clusterIdx(clusterTwoIndices) = clusterIdx(clusterTwoIndices) + ...
        size(unique(clusterIdx(clusterOneIndices)), 1);
end