get_assortative_coefficient.m

complex network复杂网络 基本参数计算

% function r=get_assortative_coefficient(Nodes)

%get assortative coefficient,see Ref[Newman,Mixing patterns in networks]
%Input:Nodes--N*N adjacent matrix,Nodes(i,j)=1;i is outdegree,j is indegree
%Output:r--assortative coefficient

N=length(Nodes);
edgeNum=nnz(Nodes);%include outEdge and inEdge,ave_degree=edgeNum/N

Outdegree=zeros(N,1);
Indegree=zeros(N,1);

for i=1:N
    Outdegree(i)=nnz(Nodes(i,:));
    Indegree(i)=nnz(Nodes(:,i));
end

%sum1 is sum(i*j)
%sum2 is sum(i+j)
%sum3 is sum(i^2+j^2)
sum1=0;
sum2=0;
sum3=0;

[Row,Col,Weight]=find(Nodes);
Len=length(Row);

for temp=1:Len
    i=Row(temp);
    j=Col(temp);
    sum1=sum1+(Indegree(j)-1)*(Outdegree(i)-1);
    sum2=sum2+(Indegree(j)-1)+(Outdegree(i)-1);
    sum3=sum3+(Indegree(j)-1)^2+(Outdegree(i)-1)^2;    
end

%for i=1:N
%    for j=1:N
%        if Nodes(i,j)>0
%            sum1=sum1+(Indegree(j)-1)*(Outdegree(i)-1);
%            sum2=sum2+(Indegree(j)-1)+(Outdegree(i)-1);
%            sum3=sum3+(Indegree(j)-1)^2+(Outdegree(i)-1)^2;
%        end
%    end
%end

r=((sum1/edgeNum)-(sum2/(2*edgeNum))^2)/((sum3/(2*edgeNum))-(sum2/(2*edgeNum))^2);

return