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Appendix F. Example MATLAB functions
% W: an n * n * c weighted adjacency matrix of the graph. It can be
%
undirected or directed, or a random walk matrix.
% LazyRate: a value between 0 and 1, the probability of moving
%
to another layer (default is 0.5)
% k: the number of vectors desired, corresponding to the k smallest
%
eigenvalues (default is all)
%
% Vout = the eigenvector matrix of out-roles
% Vin = the eigenvector matrix of in-roles
%
both n * k * c
% E = the diagonal matrix of Laplacian eigenvalues
% bigW = the large constructed matrix
%
% varargout = cell array
%
1: Vout
%
2: Vin
%
3: E
%
4: bigW
[n,m,c] = size(W);
%%%% Bind together the versions of each node in the different
%%%% layers to build a cn * cn adjacency matrix
bigW = sparse(c * n,c * n);
for i = 1:c
rowsumd = sum(W(:,:,i),2);
tempv = sparse(n,1);
tempv(rowsumd == 0) = 1;
W(:,:,i) = W(:,:,i) + diag(tempv);
rowsumd(rowsumd == 0) = 1;
tempD = diag(rowsumd);
for j = 1:c
if i == j
bigW((i-1) * n+1:i * n,(j-1) * n+1:j * n) = (1-LazyRate) * W(:,:,i);
else
bigW((i-1) * n+1:i * n,(j-1) * n+1:j * n) = LazyRate/(c-1) * tempD;
end
end
end
%%%% compute our new directed Laplacian
[DirOut,DirIn,e] = DirLaplacian(bigW,k);
Vout = zeros(n,k,c);
Vin = zeros(n,k,c);
for i = 1:c
Vout(:,:,i) = DirOut((i-1) * n+1:i * n,:);
Vin(:,:,i) = DirIn((i-1) * n+1:i * n,:);
end
varargout{1} = Vout;
varargout{2} = Vin;
varargout{3} = e;
varargout{4} = bigW;