One of the interesting features of this definition is that it need not be uniform over the whole graph, for all depends on the choice of the initial node \(n_{i}\). But in the case where the graph is sufficiently uniform, the dimension will be a constant.  Furthermore if we take a classical case, such as 3-dimensional Euclidean space, then the dimensions match. Suppose we have a regular lattice as the underlying graph, then a particular node has a cube as the set of nearest neighbours \(U_{1}\) consisting of \(3^{3} = 27\) points, and a neighbourhood \(U_{m}\) will count \((m+2)^{3}\) nodes. Therefore