  We have recently shown that the entanglement entropy of any bipartition of a
quantum state can be approximated as the sum of certain link strengths
connecting internal and external sites. The representation is useful to unveil
the geometry associated with the entanglement structure of a quantum many-body
state which may occasionally differ from the one suggested by the Hamiltonian
of the system. Yet, the obtention of these entanglement links is a complex
mathematical problem. In this work, we address this issue and propose several
approximation techniques for matrix product states, free fermionic states, or
in cases in which contiguous blocks are specially relevant. Along with this, we
discuss the accuracy of the approximation for different types of states and
partitions. Finally, we employ the link representation to discuss two different
physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear
biquadratic chain.
