drawCircGraph.m

% Draw a circular representation of a graph with the nodes ordered by degree
% Strategy: position vertices in a regular n-polygon
%
% INPUTs: adj, nxn - adjacency matrix
% OUTPUTs: plot
%
% Other routines used: degrees.m
% Last updated: Nov 29 2012

function [] = drawCircGraph(adj)

    n = size(adj, 1); % number of nodes
    [~, Y] = sort(degrees(adj)); % Y - sorted nodal indices
    angl = 2 * pi / n; % rotation angle

    for k = 1:n
        x(Y(k)) = real(exp(angl * (k - 1) * i));
        y(Y(k)) = imag(exp(angl * (k - 1) * i));
    end

    % regulate the font size with respect to graph size
    if n <= 50;
        fontsize = 10;
    elseif n > 50 && n <= 150
        fontsize = 8;
    else
        fontsize = 6;
    end

    for k = 1:n
        plot(x(k), y(k), 'k.')
        text(1.15 * x(k), 1.15 * y(k), strcat('v', num2str(k)), "fontsize", fontsize);
        hold off; hold on;
    end

    edges = find(adj > 0);
    set(gcf, 'Color', [1, 1, 1])

    for e = 1:length(edges)
        [ii, jj] = ind2sub([n, n], edges(e));
        line([x(ii) x(jj)], [y(ii) y(jj)], 'Color', 'k');
        hold off; hold on;
    end

    axis([-1.15 1.15 -1.15 1.15])
    axis square
    axis off


%!demo
%! el = preferentialAttachment(60, 1); 
%! adj = edgeL2adj(el);
%! drawCircGraph(adj)