  To resolve the controversial issue of the topological nature of the
electronic structure of YbB$_{6}$, we have made a combined study using density
functional theory (DFT) and angle resolved photoemission spectroscopy (ARPES).
Accurate determination of the low energy band topology in DFT requires the use
of modified Becke-Johnson exchange potential incorporating the spin-orbit
coupling and the on-site Coulomb interaction $U$ of Yb $4f$ electrons as large
as 7 eV. We have double-checked the DFT result with the more precise GW band
calculation. ARPES is done with the non-polar (110) surface termination to
avoid band bending and quantum well confinement that have confused ARPES
spectra taken on the polar (001) surface termination. Thereby we show
definitively that YbB$_{6}$ has a topologically trivial B 2$p$-Yb 5$d$
semiconductor band gap, and hence is a non-Kondo non-topological insulator
(TI). In agreement with theory, ARPES shows pure divalency for Yb and a $p$-$d$
band gap of 0.3 eV, which clearly rules out both of the previous scenarios of
$f$-$d$ band inversion Kondo TI and $p$-$d$ band inversion non-Kondo TI. We
have also examined the pressure-dependent electronic structure of YbB$_{6}$,
and found that the high pressure phase is not a Kondo TI but a
\emph{p}-\emph{d} overlap semimetal.
