We say that a finite, simple, undirected graph $G=(V,E)$ is $\mathbb{R}^2$-*realizable* if there is an injective map $\varphi:V\to \mathbb{R}^2$ such that for $v\neq w \in V$ we have $\{v,w\} \in E$ if and only if $|\varphi(v)-\varphi(w)| < 1$ where $|\cdot|$ denotes the Euclidean distance.

What is an example of a finite graph that is not $\mathbb{R}^2$-realizable?