53 lines
1.5 KiB
Matlab
53 lines
1.5 KiB
Matlab
% Calculating the Pearson coefficient for a degree sequence
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% INPUTs: M - matrix, square
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% OUTPUTs: r - Pearson coefficient
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% Courtesy: Dr. Daniel Whitney, circa 2006
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function prs = pearsonW(M)
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%calculates pearson degree correlation of M
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[rows,colms]=size(M);
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won=ones(rows,1);
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k=won'*M;
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ksum=won'*k';
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ksqsum=k*k';
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xbar=ksqsum/ksum;
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num=(won'*M-won'*xbar)*M*(M*won-xbar*won);
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M*(M*won-xbar*won);
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kkk=(k'-xbar*won).*(k'.^.5);
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denom=kkk'*kkk;
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prs=num/denom;
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% ALTERNATIVE .... BETTER-DOCUMENTED .... see pearson.m ....
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% Calculating the Pearson coefficient for a degree sequence
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% INPUTs: M - matrix, square
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% OUTPUTs: r - Pearson coefficient
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% source: "Assortative Mixing in Network", M.E.J. Newman, PhysRevLet 2002
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% Gergana Bounova, March 15, 2006
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% function r = pearson(M)
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%
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% [degs,~,~] = degrees(M); % get the total degree sequence
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% m = numedges(M); % number of edges in M
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% inc = adj2inc(M); % get incidence matrix for convience
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%
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% % j,k - remaining degrees of adjacent nodes for a given edge
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% % sumjk - sum of all products jk
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% % sumjplusk - sum of all sums j+k
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% % sumj2plusk2 - sum of all sums of squares j^2+k^2
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%
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% % compute sumjk, sumjplusk, sumj2plusk2
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% sumjk = 0; sumjplusk = 0; sumj2plusk2 = 0;
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% for i=1:m
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% [v] = find(inc(:,i)==1);
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% j = degs(v(1))-1; k = degs(v(2))-1; % remaining degrees of 2 end-nodes
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% sumjk = sumjk + j*k;
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% sumjplusk = sumjplusk + 0.5*(j+k);
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% sumj2plusk2 = sumj2plusk2 + 0.5*(j^2+k^2);
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% end
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%
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% % Pearson coefficient formula
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% r = (sumjk - sumjplusk^2/m)/(sumj2plusk2-sumjplusk^2/m); |