  Based on first-principles calculations and tight-binding model analysis, we
propose monolayer graphdiyne as a candidate material for a two-dimensional
higher-order topological insulator protected by inversion symmetry. Despite the
absence of chiral symmetry, the higher-order topology of monolayer graphdiyne
is manifested in the filling anomaly and charge accumulation at two corners.
Although its low energy band structure can be properly described by the
tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each
atom, the corresponding bulk band topology is trivial. The nontrivial bulk
topology can be correctly captured only when the contribution from the core
levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further
confirmed by the Wilson loop calculations. We also show that the higher-order
band topology of a monolayer graphdyine gives rise to the nontrivial band
topology of the corresponding three-dimensional material, ABC-stacked
graphdiyne, which hosts monopole nodal lines and hinge states.
