% The sum of products of degrees across all edges
% Source: "Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications", by Li, Alderson, Doyle, Willinger
% Note: The total degree is used regardless of whether the graph is directed or not.
% INPUTs: adjacency matrix
% OUTPUTs: s-metric
% Other routines used: degrees.m

function s=s_metric(adj)

[deg,~,~]=degrees(adj);
edges=find(adj>0);

s=0;
for e=1:length(edges)
  [i,j]=ind2sub([length(adj),length(adj)],edges(e));
  s=s+deg(i)*deg(j);
end


% ALTERNATIVE ================
% $$$ [deg,~,~]=degrees(adj);
% $$$ el=adj2edgeL(adj);
% $$$ 
% $$$ s=0;
% $$$ for e=1:size(el,1)
% $$$     if el(e,1)==el(e,2)
% $$$         s=s+deg(el(e,1))*deg(el(e,2))*el(e,3)*2;  % count selfloops twice
% $$$     else
% $$$         s=s+deg(el(e,1))*deg(el(e,2))*el(e,3);  % multiply by the weight for multiedges
% $$$     end
% $$$ end