  We examine two greedy heuristics - wiring and rewiring - for constructing
maximum assortative graphs over all simple connected graphs with a target
degree sequence. Counterexamples show that natural greedy rewiring heuristics
do not necessarily return a maximum assortative graph, even though it is known
that the meta-graph of all simple connected graphs with given degree is
connected under rewiring. Counterexamples show an elegant greedy graph wiring
heuristic from the literature may fail to achieve the target degree sequence or
may fail to wire a maximally assortative graph.
