  Clustering is concerned with coherently grouping observations without any
explicit concept of true groupings. Spectral graph clustering - clustering the
vertices of a graph based on their spectral embedding - is commonly approached
via K-means (or, more generally, Gaussian mixture model) clustering composed
with either Laplacian or Adjacency spectral embedding (LSE or ASE). Recent
theoretical results provide new understanding of the problem and solutions, and
lead us to a 'Two Truths' LSE vs. ASE spectral graph clustering phenomenon
convincingly illustrated here via a diffusion MRI connectome data set: the
different embedding methods yield different clustering results, with LSE
capturing left hemisphere/right hemisphere affinity structure and ASE capturing
gray matter/white matter core-periphery structure.
