This paper suggests a practical method, based on multi-domain BEM, to calculate the transmission loss of 3-dimensional silencers of subdomains comprised of different geometric and material characteristics with looped and/or cascaded connections. We previously proposed an efficient method to compute the transmission loss for 3-dimensional silencers using multi-domain BEM but its application is much difficult to those having looped subdomains [I]. Here, we adopt a method summing the impedance matrices of the subdomains with various types of connection represented by system graph. The algebraic overall condensed acoustic equations having only particle velocities on the subdomain interface boundaries as unknowns are formulated. A splitter silencer of cascaded, looped and symmetric connections as a sample problem is dealt with for the explanation and verification of the proposed method. An experimental work with the splitter silencer is performed to back up the suggested method.