  In this paper, we establish an effective edge theory to characterize
non-Hermitian edge-skin modes in higher dimensions. We begin by proposing a
bulk projection criterion to straightforwardly identify the localized edges of
skin modes. Through an exact mapping, we show that the edge-skin mode shares
the same bulk-boundary correspondence and localization characteristics as the
zero-energy edge states in a Hermitian semimetal under open-boundary
conditions, bridging the gap between non-Hermitian edge-skin effect and
Hermitian semimetals. Another key finding is the introduction of ``skewness,''
a term we proposed to describe the characteristic decay direction of skin mode
from the localized edge into the bulk. Remarkably, we demonstrate that skewness
is an intrinsic quantity of the skin mode and can be analytically determined
using the corresponding cylinder-geometry bulk Hamiltonian, without requiring
any boundary details. Furthermore, we reveal that in the edge-skin effect, the
spectrum exhibits anomalous spectral sensitivity to weak local disturbances, a
feature that crucially distinguishes it from the corner-skin effect.
