  The level structure of nuclei offers a large amount and variety of
information to improve our knowledge of the strong interaction and of
mesoscopic quantum systems. Gamma spectroscopy is a powerful tool to perform
such studies: modern gamma multi-detectors present increasing performances in
terms of sensitivity and efficiency, allowing to extend ever more our ability
to observe and characterize abundant nuclear states. For instance, the
high-spin part of level schemes often reflects intriguing nuclear shape
phenomena: this behaviour is unveiled by high-fold experimental data analysed
through multi-coincidence spectra, in which long deexcitation cascades become
observable. Determining the intensity of newly discovered transitions is
important to characterize the nuclear structure and formation mechanism of the
emitting levels. However, it is not trivial to relate the apparent intensity
observed in multi-gated spectra to the actual transition intensity. In this
work, we introduce the basis of a formalism affiliated with graph theory: we
have obtained analytic expressions from which data-analysis methods can
eventually be derived to recover this link in a rigorous way.
