% At first there are only m nodes and no edge, then the m+1st node is
% connected with the above m nodes
% usage: Nodes = BA(N,m)
% the parameter:N----network size
% m----a new node with m new edges
% can randomly initialize the N and the m by yourself
% the diagonal elements of the matrix also equal to -degree
% Nodes----the final coupling matrix
% The following message(s) may not be displayed correctly for they contain Chinese charactors.
% list----生成的一个辅助向量，该向量中的元素为每条边端点的节点。for example, 假设网络中节点4的度为7，则在list向量中会存在7个4，而这7个4的位置不一定是连续在一起的。
% preferential attachment体现在随机的从list向量中选取元素，选中哪个元素，该元素表示的节点即被选中。由于list向量中每个节点的个数与它的度有关，因此，度越大的点被选中的概率越大。
function [Nodes,Cii]=BA(N,m)
% N=10,m=3;
Nodes=zeros(N);
Cii=zeros(1,N);
t=zeros(1,N);
%Nodes=sparse(N);
for i=1:m
Nodes(i,m+1)=1;
Nodes(m+1,i)=1;
list(i)=i;
end
for i=m+1:2*m
list(i)=m+1;
end
for n=m+2:N % start from m+2 to grow the network
t=2*m*(n-m-1) ; % for list, every time t increases 2m
% t=m*(n-m-1);
for i=1:m
list(t+i)=n; % in the list, every time the above m is n, it represents that the nth nodes is connected to other m nodes
end
k=1;
while k<m+1 % grow other m nodes
p(k)=round((t+1)*rand(1)); % random choose an integer from 1~N
if p(k)>0&p(k)<(t+1)
if Nodes(n,list(p(k)))==0
list(t+m+k)=list(p(k));
Nodes(n,list(p(k)))=1;
Nodes(list(p(k)),n)=1;
k=k+1;
end %end for j
end %end for k
end %end for n
end
%Write_Sparse_Matrix(Nodes,['BA',num2str(N),'.txt']);
%Write_into_Pajek(Nodes,['BA',num2str(N),'.net']);
% for i=1:N
% Nodes(i,i)=sum(Nodes(:,i));
% Cii(i)=Nodes(i,i);
% end
for i=1:N
Cii(i)=sum(Nodes(:,i));
t(i)=list(i)
end
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