1Sk = 0 otherwise. It follows from (iii) that for the ideal case where we have d completely separate populations (and the node degrees are similar), individuals from the same population map into the same point in an embedding defined by the d first eigenvectors of ℒ. For example, if d = 3, the N − d embedding matrix for N = 6 individuals could have the form U=[D1/21S1,D1/21S2,D1/21S3]=(d11/200d21/200d31/2000d41/200d51/2000d61/2)≈(100100100010010001).
