  Based on first-principles calculations and effective model analysis, a Dirac
nodal-net semimetal state is recognized in AlB$_2$-type TiB$_2$ and ZrB$_2$
when spin-orbit coupling (SOC) is ignored. Taking TiB$_2$ as an example, there
are several topological excitations in this nodal-net structure including
triple point, nexus, and nodal link, which are protected by coexistence of
spatial-inversion symmetry and time reversal symmetry. This nodal-net state is
remarkably different from that of IrF$_4$, which requires sublattice chiral
symmetry. In addition, linearly and quadratically dispersed two-dimensional
surface Dirac points are identified as having emerged on the B-terminated and
Ti-terminated (001) surfaces of TiB$_2$ respectively, which are analogous to
those of monolayer and bilayer graphene.
