  Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement
entropy of sets of neighborhoods is computed. For a subsystem composed of a
single neighborhood, an analytical expression is provided by the decomposition
in irreducible submodules of the Terwilliger algebra of $J(n,k)$ embedded in
two copies of $\mathfrak{su}(2)$. For a subsytem composed of multiple
neighborhoods, the construction of a block-tridiagonal operator which commutes
with the entanglement Hamiltonian is presented, its usefulness in computing the
entropy is stressed and the area law pre-factor is discussed.
