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.
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