between two terminals, are there some good ways to find the ``topologically equivalent'' circuit?
Well, I'm not sure there's a systematic method... this mostly comes with practice... the key thing to remember is that all points connected by a wire are at the same potential, and you can bend and morph the wire, and rotate circuit elements, in any way so long as you keep the relationships between the potentials and elements intact. After a while you will find you will easily recognize equivalent patterns. You'll get more practice as we go along.