Which would not have a unique solution (M would be singular) if {y -x : y ∈ N (x)} did not form a basis. Condition 3 is necessary, but not sufficient, for condition 4, which ensures that the gradient can be followed as well as approximated on the graph. These conditions serve to narrow down the choice of graph construction. For example, given the goal of defining a neighbourhood, it might be tempting to use the set of n nearest neighbours of each point N (n) (x) to define the n-nearest-neighbour graph: