  We carry out three-body-model calculations for a proton-rich Borromean
nucleus $^{17}$Ne by assuming a $^{15}$O + $p$ + $p$ structure. To this end, we
use a density-dependent contact interaction between the valence protons,
explicitly treating also the Coulomb interaction. We find that the two-particle
density distribution for $^{17}$Ne is similar to that for $^{16}$C, which has
two valence neutrons outside the $N$ = 8 core. That is, the two protons take a
spatially compact configuration, while the Coulomb repulsion plays a minor
role. This indicates that there is a strong diproton correlation in the ground
state of the $^{17}$Ne nucleus. We also show that the Coulomb interaction
reduces the expectation value of the proton-proton interaction by about 14\%.
