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

We develop recursive relations among abundances in an r-process network evolving neutron captures, photodisintegrations and beta decays 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 in different astrophysical environments. We also illustrate how they can be used to follow complex reaction flows quantitatively in an evolving r-process network through the concept of {\em contribution paths}. Such contribution paths show how particular reactions govern the evolution of abundance features during the nucleosynthesis and, consequently, can clarify the role of key nuclear data and astrophysical environments in that evolution. The Python open-source package that implements the tool is freely available.