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• We introduce the novel concept of decomposing the FRFs into paths. • The concept is based upon the FRFs, not upon transmissibilities as in GTDT. • The methodology can realize clear visualization of the contents of the FRFs. • It can evaluate the contributions of paths to the FRFs quantitatively. • The presented approach will promise to solve NVH problems. Frequency response functions (FRFs) lie within the framework of the linear response theory in elastic structures. In FRFs, the inputs/outputs relationships are strictly determined, but there is no way of knowing how waves are propagated and converted from the input signals into the output signals. Thus, the wave propagation between the inputs and outputs cannot be clearly understood by the FRFs. In this study, we succeeded in visualizing the contents of these FRFs by decomposing them into geometric paths using a signal flow graph. Moreover, we succeeded in quantitatively evaluating the contributions of the paths to these FRFs. In terms of application, when the noise or vibration of industrial products is loud and unpleasant, this analytical methodology can help identify the cause behind such nuisance by using paths in contribution to FRFs. This methodology is expected to pave the way for taking quantitative countermeasures on the basis of analytical results. [ABSTRACT FROM AUTHOR]