function [m,Adj,X,Y]=erdosRenyi(nv,p)

%Funciton [Adj,X,Y]=edosRenyi (nv,p)

%generates a random graph based on the Erdos and Renyi algoritm

%where all possible pairs of 'nv' nodes are connected with probability 'p'.

%Nodes are distributed in space on a circular regular latice.  

%See the function circle.m by Zhenhai Wang <zhenhai@ieee.org>. For more details

%see under  MATLAB Central >  

%           File Exchange > Graphics > Specialized Plot and Graph Types > Draw a circle.

%

%Edited by LIU JIE 2005-01-19 Email: liujie@jerry.cn

center=[0,0];

theta=linspace(0,2*pi,nv);%devide the circle into 'nv' parts to put the vertices onto it! using polar coordinate!

rho=ones(1,nv);%the more nv, the larger the circle radius!

[X,Y] = pol2cart(theta',rho');%transfer polar cooedinate to decart coordinate!

X=X+center(1);

Y=Y+center(2);%Registering the TWO new vectors coordinates by X,Y!

P=nchoosek(1:nv,2);%choose two elements from 1 to nv, registered as a matrix of nv*2;

C=(rand(length(P),1)<=p);% Randomly generate a P_equal-length column vector and reserving the necessary links should added

                        % which are determinied by parability 'p', then registered it by 'C'.

Adj=sparse(P(:,1),P(:,2),C);% Creat the Adjacent Materix by a sparse matrix type.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Convert the Adj to a Symmetry Square Matrix! 2005-04-19

%Symmetry a non-square Matrix.

m=full(Adj);

m(nv,nv)=[0];

for i=1:nv

   for j=1:nv

       if (i>=j)

          m(j,i)=m(i,j);

          m(i,j)=m(i,j);

       else

       end

   end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Plotting section (comment to avoid plotting)

f=figure;

set(f,'Color','w')

gplot(Adj,[X Y],'k-')

hold on;

h=scatter(X,Y,5,'y','filled');

set(gca,'Visible','Off');

set(h,'LineWidth',2,...

       'MarkerEdgeColor','k',...

       'MarkerSize',8);

axis square

%end of plotting section