  Numerical computations and methods have become increasingly crucial in the
study of spin foam models across various regimes. This paper adds to this field
by introducing new algorithms based on tensor network methods for computing
amplitudes, focusing on topological SU(2) BF and Lorentzian EPRL spin foam
models. By reorganizing the sums and tensors involved, vertex amplitudes are
recast as a sequence of matrix contractions. This reorganization significantly
reduces computational complexity and memory usage, allowing for scalable and
efficient computations of the amplitudes for larger representation labels on
standard consumer hardware--previously infeasible due to the computational
demands of high-valent tensors.
  We apply these tensor network algorithms to analyze the characteristics of
various vertex configurations, including Regge and vector geometries for the
SU(2) BF theory, demonstrating consistent scaling behavior and differing
oscillation patterns. Our benchmarks reveal substantial improvements in
computational time and memory allocations, especially for large representation
labels. Additionally, these tensor network methods are applicable to generic
2-complexes with multiple vertices, where we introduce partial-coherent vertex
amplitudes to streamline the computations. The implementation of these
algorithms is available on GitHub for further exploration and use.
