Exhibit: Dimensions of graphs

Various dimensions have been introduced for graphs. Here is a geometrical definition given in P. Erdoes, F. Harary and W. Tutte: On the dimension of a graph: Mathemetrika 12, 1965, 118-122: [PDF].

The dimension of a graph is the minimum number n such that G can be embedded in Euclidean space En with every edge of G having length 1.