Example 1.1.6.11. Let $G$ be a directed graph and let $G_{\bullet }$ denote the associated simplicial set of dimension $\leq 1$ (Remark 1.1.6.10). Then $G_{\bullet }$ has dimension $\leq 0$ if and only if the edge set $\operatorname{Edge}(G)$ is empty. In this case, $G_{\bullet }$ can be identified with the constant simplicial set $\underline{\operatorname{Vert}(G)}$.
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