While nonlinear peptide natural products such as Vancomycin and Daptomycin are among the most effective antibiotics, the computational techniques for sequencing such peptides are still in their infancy. Previous methods for sequencing peptide natural products are based on Nuclear Magnetic Resonance spectroscopy and require large amounts (milligrams) of purified materials. Recently, development of mass spectrometry-based methods has enabled accurate sequencing of nonlinear peptide natural products using picograms of material, but the question of evaluating statistical significance of Peptide Spectrum Matches (PSM) for these peptides remains open. Moreover, it is unclear how to decide whether a given spectrum is produced by a linear, cyclic, or branch-cyclic peptide. Surprisingly, all previous mass spectrometry studies overlooked the fact that a very similar problem has been successfully addressed in particle physics in 1951. In this work, we develop a method for estimating statistical significance of PSMs defined by any peptide (including linear and nonlinear). This method enables us to identify whether a peptide is linear, cyclic, or branch-cyclic, an important step toward identification of peptide natural products.