function [slope,R2,intercept] = Plot_Degree_Distribution(adjacency,name,save)
% Plot degree distribution given a adjacency matrix
%
%       [slope,R2,intercept] = Plot_Degree_Distribution(adjacency,name,save)
%
% Jesus Perez-Ortega
% modified Nov 2018
% modified June 2019

switch nargin
    case 1
        name = '';
        save = false;
    case 2
        save = false;
end

cells=length(adjacency);
links=sum(adjacency,1);

if ~links
    warning('There are no links.')
    return;
end

% Get links histogram (only neurons with at least one link)
links_1=links(links>0);
N=length(links_1);
nbins = round(log2(N)+1);   % Sturges rule
%nbins = 2*iqr(links_1)*N^(-1/3);    % Freedman-Diaconis rule for heavy tailed

[y,x]=hist(links_1,nbins);
y=y/sum(y);

% Plot power law fit
try
    [slope, intercept, R2] = Fit_Power_Law(x',y');
catch
    slope=NaN;
    intercept=NaN;
    R2=NaN;
    return
end
xfit=min(x):(max(x)-min(x))/100:max(x);
yfit=intercept*xfit.^(slope);

% Plot Links
Set_Figure(['Links - ' name],[0 0 600 200]);
Set_Axes(['Links ' name],[0 0 1 1])
plot(find(links>0),links_1,'ob'); hold on
plot(find(links==0),links(links==0),'or')
set(gca,'xlim',[0 cells],'ylim',[0 max(links)+1])
title(name); xlabel('# neuron'); ylabel('Count of links')

% Save
if(save)
    Save_Figure([name ' - Links' ]);
end

% Plot linear links histogram
Set_Figure(['Distribution - ' name],[0 0 600 200]);
Set_Axes(['Links ' name],[0 0 0.5 1])
plot(x,y,'ob','markersize',10); hold on
plot(xfit,yfit,'k')
xlabel('k'); ylabel('P(k)'); title(['Degree distribution - ' name])

% Write the coefficients
text(max(x)/2,max(y)*0.8,['\lambda=' num2str(-slope,'%0.1f')],'FontSize',14,'FontWeight','bold')
text(max(x)/2,max(y)*0.6,['R^2=' num2str(R2,'%0.3f')],'FontSize',14,'FontWeight','bold')

% Plot loglog links histogram
Set_Axes(['HistLinksPL ' name],[0.5 0 0.5 1])
loglog(x,y,'ob','markersize',10); hold on
loglog(xfit,yfit,'k')
xlabel('k'); ylabel('P(k)'); title(['Degree distribution - ' name])

% Save
if(save)
    %Save_Figure([name ' - Distribution']);
    Save_Figure([name ' - Distribution'],'eps');
end