  A non-Hermitian system is characterized by the violation of energy
conservation. As a result of unbalanced gain or loss in the forward and
backward directions due to non-reciprocal couplings, the eigenmodes of such
systems exhibit extreme localization, also known as non-Hermitian skin effect
(NHSE). This work explores unconventional scenarios where the interplay of
multiple asymmetric couplings can cause the NHSE to vanish, with the admittance
spectra taking identical dispersion under open boundary conditions (OBC) and
periodic boundary conditions (PBC). This is unlike known non-Hermitian models
where the NHSE vanishes only when the non-Hermiticity is turned off. We derive
general conditions for the NHSE, with the overall eigenmode localization
determined by the geometric mean of the cumulative contributions of all
asymmetric coupling segments. In the limit of large unit cells, our results
provide a route towards the NHSE caused by asymmetric hopping textures, rather
than single asymmetric hoppings alone. Furthermore, our generalized model can
be transformed into a square-root lattice simply by tuning the coupling
capacitors, where the topological edge states occur at a non-zero admittance,
in contrast to the zero-admittance states of conventional topological
insulators. We provide explicit electrical circuit setups for realizing our
observations, which also extend to other established platforms such as
photonics, mechanics, optics and quantum circuits.
