www.pudn.com > Powerlaw_with_Expected_Exponent.rar > Powerlaw_with_Expected_Exponent.m

function Nodes=Powerlaw_with_Expected_Exponent(N,m,gama,node_attribution) 
%This program generates a power law degree distribution graph with expected gama 
%Ref[Universal behavior of load distribution in Scale free networks,PRL V87,2001,12] 
%Input: 
%N--the number of nodes 
%m--the mean degree =2m 
%gama--the expected exponent,blong to (2,infinit),whose corelation with the control 
%      parameter alfa is: gama=1+1/alfa,where alfa is [0,1) 
%node_attribution--if node_attribution==1,Nodes is adjacent matrix; if 
%                   node_attribution=2,Nodes is adjacent list. 
%Output 
%Nodes--return the adjacent matrix if node_attribution=1.the adjacent list 
%       if node_attribution=2 
% 
 
 
 
if node_attribution==1 
    Nodes=zeros(N,N); 
    p=zeros(N,1); 
    pp=zeros(N,1); 
    node_1_Len=zeros(N,1); 
    node_2_Len=zeros(N,1); 
    alfa=1/(gama-1); 
    edge_num=N*m; 
     
    %1.get nodes' weight 
    for i=1:N 
        p(i)=1/(i^alfa);         
    end 
    %2.normalized node weights 
    sum_p=sum(p); 
    pp(1)=p(1)/sum_p; 
    for i=2:N 
        pp(i)=pp(i-1)+p(i)/sum_p;         
    end 
     
    %3.add edge 
    for i=1:edge_num 
       %i 
       ADD_ONE_EDGE=0; 
       while ADD_ONE_EDGE==0 
            node_1_Len=find(pp>rand(1));  
            node_1=node_1_Len(1); 
            node_2_Len=find(pp>rand(1)); 
            node_2=node_2_Len(1); 
            while node_2==node_1%avoid self-loop 
                node_2_Len=find(pp>rand(1)); 
                node_2=node_2_Len(1); 
            end 
            if Nodes(node_1,node_2)==0 
                Nodes(node_1,node_2)=1; 
                Nodes(node_2,node_1)=1; 
                ADD_ONE_EDGE=1; 
            else 
                ADD_ONE_EDGE=0; 
            end%Nodes(node_1,node_2) 
       end%while ADD_ONE_EDGE==0 
    end% for i=1:edge_num     
end%node_attribution 
 
 
if TEST==1 
    t=toc 
    for i=1:N 
        Degree(i)=nnz(Nodes(i,:)); 
    end 
    plot_distribution(Degree,Line_color,1); 
    fname=['PLRG',num2str(N),'k',num2str(m),'gama',num2str(gama)]; 
    Write_Sparse_Matrix(Nodes,[fname,'.adj']); 
    Write_into_Pajek(Nodes,[fname,'.net']); 
end 
 
return