Hey thanks for the video! I recently read Homotopy in Mendelson's Introduction to Topology, and this video helped in grasping the "math" in whole of the discussion and abstraction of paths and connectedness.
The fundamental group is a homotopy to the diagonal entries ( one fundamental group for each diagonal entry) in the subroutine call from-to matrix via Warshalls algorithm. The diagonal entry indicates if a subroutine ever calls itself(loops back to itself)!!! Clue: cf AI networks and how this applies!!!