% Count the number of connected triples in a graph.
% Note: works for undirected graphs only
%
% INPUTs: adjacency matrix, nxn
% OUTPUTs: integer - number of connected triples
%
% Other routines used: kneighbors.m, cycles3.m
% GB: last updated, October 4, 2012

function c=numConnTriples(adj)

c=0;  % initialize

for i=1:length(adj)
    neigh=kneighbors(adj,i,1);
    if length(neigh)<2; continue; end  % handle leaves, no triple here
    c=c+nchoosek(length(neigh),2);
end

c=c-2*cycles3(adj); % due to the symmetry triangles repeat 3 times
                   %                        in the nchoosek count


% alternative
% def numConnTriples(L):
% 
% % input: adjacency list
% % outputs: number of connected triples
% 
% c=0;      % initialize number of connected triples
% 
% for i=1:length(L)
%   neigh = L{i}
%   if length(neigh)<2: continue; end
%   c = c + nchoosek(length(neigh),2);
% end
% 
% c = c - 2*cycles3(adjL2adj(L));