dotMatrixPlot.m

% Draws the matrix as a column/row sorted square dot-matrix pattern.
%
% INPUTs: adj (nxn) - adjacency matrix representation of the graph
% OUTPUTs: plot
%
% Note 1: Change colors and marker types in lines 64, 71, 78, 85 and 92, 99
% Note 2: Easy to add/remove different node orderings to/from the plot
%
% Other routines used: degrees.m, sortNodesByMaxNeighborDegree.m,
%                      eigenCentrality.m, newmanEigenvectorMethod.m,
%                      nodeBetweennessFaster.m, newmanGirvan.m, closeness.m
% Last updated: April 14 2015

function [] = dotMatrixPlot(adj)

    n = size(adj, 1);
    %markersize=ceil(n/50); % scale for plotting purposes
    markersize = 3;
    deg = degrees(adj);

    Yd = sortNodesByMaxNeighborDegree(adj); % degree centrality
    [~, Yb] = sort(nodeBetweennessFaster(adj)); % node betweenness centrality
    [~, Yec] = sort(eigenCentrality(adj)); % eigen-centrality
    [~, Yc] = sort(closeness(adj)); % closeness

    % sort by module
    modules = newmanEigenvectorMethod(adj);
    % sort modules by length
    mL = zeros(1, length(modules));

    for i = 1:length(modules);
        mL(i) = length(modules{i});
    end

    [~, Yms] = sort(mL);

    % sort nodes by degree inside modules
    Ym = [];

    for mm = 1:length(modules)
        module = modules{Yms(mm)};
        deg_module = deg(module);
        [~, Yds] = sort(deg_module);
        module_sorted = module(Yds);

        for xx = 1:length(module_sorted)
            Ym = [Ym module_sorted(xx)];
        end

    end

    mods = newmanGirvan(adj, 4); % enter the expected number of communities

    % sort modules by length
    mL = zeros(1, length(mods));

    for i = 1:length(mods);
        mL(i) = length(mods{i});
    end

    [~, Yms] = sort(mL);
    Ymb = [];

    for mm = 1:length(mods)
        module = mods{Yms(mm)};
        deg_module = deg(module);
        [~, Yds] = sort(deg_module);
        module_sorted = module(Yds);

        for xx = 1:length(module_sorted)
            Ymb = [Ymb module_sorted(xx)];
        end

    end

    set(gcf, 'Color', [1 1 1])
    subplot(3, 2, 1)
    spy(adj(Yd, Yd), 'k.', markersize)
    title('ordered by degree', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square

    subplot(3, 2, 2)
    spy(adj(Yb, Yb), 'k.', markersize)
    title('ordered by betweenness', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square

    subplot(3, 2, 3)
    spy(adj(Yec, Yec), 'k.', markersize)
    title('ordered by eigen-centrality', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square

    subplot(3, 2, 4)
    spy(adj(Yc, Yc), 'k.', markersize)
    title('ordered by closeness', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square

    subplot(3, 2, 5)
    spy(adj(Ym, Ym), 'k.', markersize)
    title('ordered by module - eigenvector method', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square

    subplot(3, 2, 6)
    spy(adj(Ymb, Ymb), 'k.', markersize)
    title('ordered by module - Newman-Girvan', 'FontWeight', 'bold')
    axis([0 n 0 n]);
    set(gca, 'YDir', 'normal')
    axis square


%!demo
%! adj = randomModularGraph(21, 3, log(100)/100, 5);
%! dotMatrixPlot(adj)