  This paper offers a review of recent studies on the entanglement of
free-fermion systems on graphs that take advantage of methods pertaining to
signal processing and algebraic combinatorics. On the one hand, a parallel with
time and band limiting problems is used to obtain a tridiagonal matrix
commuting with the chopped correlation matrix in bispectral situations and on
the other, the irreducible decomposition of the Terwilliger algebra arising in
the context of $P$-polynomial association schemes is seen to yield a
simplifying framework.
