  In this study, we investigate in detail the photospheric magnetic structure
of 98 coronal holes using line-of-sight magnetograms of SDO/HMI, and for a
subset of 42 coronal holes using HINODE/SOT G-band filtergrams. We divided the
magnetic field maps into magnetic elements and quiet coronal hole regions by
applying a threshold at $\pm 25$ G. We find that the number of magnetic bright
points in magnetic elements is well correlated with the area of the magnetic
elements (cc=$0.83\pm 0.01$). Further, the magnetic flux of the individual
magnetic elements inside coronal holes is related to their area by a power law
with an exponent of $1.261\pm 0.004$ (cc=$0.984\pm 0.001$). Relating the
magnetic elements to the overall structure of coronal holes, we find that on
average ($69\pm 8$) % of the overall unbalanced magnetic flux of the coronal
holes arises from long-lived magnetic elements with lifetimes > 40 hours. About
($22\pm 4$) % of the unbalanced magnetic flux arises from a very weak
background magnetic field in the quiet coronal hole regions with a mean
magnetic field density of about 0.2 to 1.2 G. This background magnetic field is
correlated to the flux of the magnetic elements with lifetimes of > 40 h
(cc=$0.88\pm 0.02$). The remaining flux arises from magnetic elements with
lifetimes < 40 hours. By relating the properties of the magnetic elements to
the overall properties of the coronal holes, we find that the unbalanced
magnetic flux of the coronal holes is completely determined by the total area
that the long-lived magnetic elements cover (cc=$0.994\pm 0.001$).
