Graph-based recursive relations for computing and analyzing r-process abundances.

We develop recursive relations among abundances in an r-process network through the use of the matrix-tree and matrix-forest theorems. Since these theorems are based on results from graph theory, we term the relations the GrRproc (Graphical R-process) relations. We validate the relations by using them to compute r-process abundances in network calculations at different astrophysical environments. We also briefly illustrate how they can be used to follow complex reaction flows in an evolving r-process network and to clarify the role of key nuclear and reaction data in that evolution.This work was supported by NASA grant 80NSSC20K0338 and NSF Grant PHY-2020275 (Network for Neutrinos, Nuclear Astrophysics and Symmetries (N3AS)).