kminNeighbors.m

% Finds the number of "kmin"-neighbors (k links away at a minimum) for every node
% If nodes are k-links away due to loops (so they appear as m-neighbours, m<k),
%                                                            they are not counted
%
% INPUTS: adjacency matrix (nxn), start node index, k - number of links
% OUTPUTS: vector of "kmin"-neighbor indices
%
% Last update: Oct 7 2012

function kneigh = kminNeighbors(adj, ind, k)

    close_neighbors = [];

    adjk = adj;

    for i = 1:k - 1
        close_neighbors = [close_neighbors find(adjk(ind, :) > 0)];
        adjk = adjk * adj;
    end

    kneigh = setdiff(find(adjk(ind, :) > 0), [close_neighbors ind]);


%!test
%!shared T
%! T = load_test_graphs();
%!assert(kminNeighbors(T{4}{2},1,3),[5, 6])
%!assert(kminNeighbors(T{4}{2},3,1),[1, 2, 4])
%!assert(kminNeighbors(T{4}{2},3,2),[5, 6])

%!demo
%! bowtie=[0 1 1 0 0 0; 1 0 1 0 0 0; 1 1 0 1 0 0; 0 0 1 0 1 1; 0 0 0 1 0 1; 0 0 0 1 1 0];
%! kminNeighbors(bowtie, 1, 1)
%! kminNeighbors(bowtie, 1, 2)
%! kminNeighbors(bowtie, 1, 3)