Neon (Ne) has an atomic number of 10. Therefore, the $Ne_{2}$ molecule contains a total of 20 electrons (10 + 10).
For molecules with more than 14 electrons (like $O_{2}$ and $Ne_{2}$), the energy order of molecular orbitals is: $$\sigma_{1s} < \sigma_{1s}^{*} < \sigma_{2s} < \sigma_{2s}^{*} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi_{2p_x}^{*} = \pi_{2p_y}^{*} < \sigma_{2p_z}^{*}$$
Distributing 20 electrons: $$\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2, \pi_{2p_x}^{*2}, \pi_{2p_y}^{*2}, \sigma_{2p_z}^{*2}$$
The last electrons enter the $\sigma_{2p_z}^{*}$ orbital (often denoted as $\sigma_{2p}^{*}$). Thus, the HOMO is $\sigma_{2p}^{*}$.
Final Answer: A
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