  We prove that the accumulation points of a sequence of graphs
$G_1,G_2,G_3,\ldots$ with respect to the cut-distance are exactly the weak$^*$
limit points of subsequences of the adjacency matrices (when all possible
orders of the vertices are considered) that minimize the entropy over all
weak$^*$ limit points of the corresponding subsequence. In fact, the entropy
can be replaced by any map $W\mapsto \int\int f(W(x,y))$, where $f$ is a
continuous and strictly concave function. Our proofs are elementary, and do not
use the regularity lemma.
