基于Matlab的BA无标度网络拓扑生成算法，BA模型有两个重要特性：增长特性和优先连接特性.rar

% This is the BA_Scale Model by Fan Jin. % 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=25,m=2; 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