The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be embedded with every edge length equal to 1 and every vertex position distinct (but where edges may cross or overlap and points may lie on edges that are not incident on them; Erdős et al. 1965).

metric dimension | unit-distance graph