  Three-dimensional topological gapless phases have attracted significant
attention due to their unique electronic properties. A flagship example are
Weyl semimetals, which require breaking time-reversal or inversion symmetry. In
two dimensions, the dimensionality reduction requires imposing an additional
symmetry, thereby weakening the phase. Like its three-dimensional counterpart,
these two-dimensional Weyl semimetals present edge states directly related to
Weyl nodes. The direct comparison with the edge states in zigzag-like
terminated graphene ribbons is unavoidable, offering the question of how robust
these states are and their differences. Here we benchmark the robustness of the
edge states in two-dimensional Weyl semimetals without inversion symmetry with
those present in zigzag graphene ribbons. Our results show that, despite having
a similar electronic band structure, the edge states of two-dimensional Weyl
semimetal are more robust against vacancies than graphene ribbons. We attribute
this enhanced robustness to a crucial role of the spin degree of freedom in the
former case
