function max_flow=ff_max_flow(source,sink,capacity,nodes_number)
current_flow=zeros(nodes_number,nodes_number);
max_flow=0;
augmentpath = bfs_augmentpath(source,sink,current_flow,capacity,nodes_number);
%bfs_augmentpath(2,6,current_flow,capacity,6)
while ~isempty(augmentpath)
% if there exits a augment path, update teh current_flow
increment = inf;
for i=1:length(augmentpath)-1
increment=min(increment, capacity(augmentpath(i),augmentpath(i+1))-current_flow(augmentpath(i),augmentpath(i+1)));
end
%now increase the current_flow
for i=1:length(augmentpath)-1
current_flow(augmentpath(i),augmentpath(i+1))=current_flow(augmentpath(i),augmentpath(i+1))+increment;
current_flow(augmentpath(i+1),augmentpath(i))=current_flow(augmentpath(i+1),augmentpath(i))-increment;
end
max_flow=max_flow+increment;
augmentpath = bfs_augmentpath(source,sink,current_flow,capacity,nodes_number);% try to find new augment path
end
